How do you use the limit process to find the area of the region between the graph #y=x^2x^3# and the xaxis over the interval [1,0]?
# int_(1)^0 \ x^2x^3 \ dx = 7/12 #
By definition of an integral, then
That is
And so:
Using the standard summation formula:
we have:
And this is now a trivial limit to evaluate, so:
Using Calculus
If we use Calculus and our knowledge of integration to establish the answer, for comparison, we get:
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To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:
To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:
1.To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine theTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

SplitTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integralTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region intoTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral ofTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of theTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimallyTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function (To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally smallTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( yTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallelTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = xTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to theTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2 To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxisTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  xTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis. 2To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis. 2.To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 \To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

ApproximateTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 )To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate theTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over theTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the areaTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the intervalTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of eachTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangleTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle byTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1,To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplyingTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying itsTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its widthTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]),To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (whichTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), whichTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approachesTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which representsTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero)To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents theTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) byTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the areaTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by theTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under theTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height ofTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curveTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of theTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between \To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function atTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at someTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some pointTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) andTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point withinTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within thatTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangleTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0\To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle. 3To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).
To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle. 3.To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).
2.To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum upTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

ToTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up theTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To setTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areasTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set upTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas ofTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up theTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of allTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integralTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all theseTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral,To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectanglesTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrateTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to getTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the functionTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get anTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function (To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximationTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( yTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation ofTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y =To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of theTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = xTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total areaTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area. To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2 To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area. 4To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  xTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area. 4.To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

TakeTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limitTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 \To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit asTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) withTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as theTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respectTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the widthTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect toTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width ofTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to (To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of theTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( xTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approachesTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x \To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zeroTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x )To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero toTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) overTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to getTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over theTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get theTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval \To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact areaTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1,To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
MathemTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
MathematicallyTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically,To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]).To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the areaTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). ThisTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area canTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This givesTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can beTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives youTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressedTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expressionTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as theTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: \To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral ofTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\intTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of theTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (yTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y =To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = xTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0}To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  xTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (xTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2 To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) overTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  xTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over theTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval \To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) \To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).
To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:
 Split the region into infinitesimally small rectangles parallel to the xaxis.
 Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.
 Sum up the areas of all these rectangles to get an approximation of the total area.
 Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]\To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).
3To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:
 Split the region into infinitesimally small rectangles parallel to the xaxis.
 Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.
 Sum up the areas of all these rectangles to get an approximation of the total area.
 Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).
3.To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:
 Split the region into infinitesimally small rectangles parallel to the xaxis.
 Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.
 Sum up the areas of all these rectangles to get an approximation of the total area.
 Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate theTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \textTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integralTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{AreaTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area}To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} =To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \intTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{nTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \toTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \inTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0}To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty}To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (xTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sumTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{iTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2 To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3)To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{nTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) \To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n}To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) ,To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} fTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dxTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(xTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i)To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \DeltaTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \fracTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x \To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
whereTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where (To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( fTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(xTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3} To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_iTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) \To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \fracTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) )To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is theTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the valueTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value ofTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of theTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the functionTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \rightTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function atTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some pointTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point withinTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within theTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (iTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0}To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subintervalTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, andTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ =To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and (To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \leftTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \DeltaTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x )To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) isTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the widthTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width ofTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of eachTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subintervalTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3} To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval.To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. InTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \fracTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In thisTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this caseTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case,To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, (To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \DeltaTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta xTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4}To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x \To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x )To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \rightTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x ) isTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \right) To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x ) is (\To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \right)  \To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x ) is (\fracTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \right)  \leftTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x ) is (\frac{To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \right)  \left(To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x ) is (\frac{1To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \right)  \left( \To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x ) is (\frac{1}{To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \right)  \left( \fracTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x ) is (\frac{1}{nTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \right)  \left( \frac{To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x ) is (\frac{1}{n}\To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \right)  \left( \frac{(To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x ) is (\frac{1}{n})To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \right)  \left( \frac{(1To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x ) is (\frac{1}{n}) sinceTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \right)  \left( \frac{(1)^To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x ) is (\frac{1}{n}) since theTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \right)  \left( \frac{(1)^3To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x ) is (\frac{1}{n}) since the intervalTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \right)  \left( \frac{(1)^3}{To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x ) is (\frac{1}{n}) since the interval \To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \right)  \left( \frac{(1)^3}{3To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x ) is (\frac{1}{n}) since the interval ([To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \right)  \left( \frac{(1)^3}{3} To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x ) is (\frac{1}{n}) since the interval ([1To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \right)  \left( \frac{(1)^3}{3}  \To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x ) is (\frac{1}{n}) since the interval ([1,0To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \right)  \left( \frac{(1)^3}{3}  \fracTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x ) is (\frac{1}{n}) since the interval ([1,0]\To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \right)  \left( \frac{(1)^3}{3}  \frac{To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x ) is (\frac{1}{n}) since the interval ([1,0])To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \right)  \left( \frac{(1)^3}{3}  \frac{(To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x ) is (\frac{1}{n}) since the interval ([1,0]) hasTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \right)  \left( \frac{(1)^3}{3}  \frac{(1)^To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x ) is (\frac{1}{n}) since the interval ([1,0]) has aTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \right)  \left( \frac{(1)^3}{3}  \frac{(1)^4To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x ) is (\frac{1}{n}) since the interval ([1,0]) has a widthTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \right)  \left( \frac{(1)^3}{3}  \frac{(1)^4}{To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x ) is (\frac{1}{n}) since the interval ([1,0]) has a width of To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \right)  \left( \frac{(1)^3}{3}  \frac{(1)^4}{4}To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x ) is (\frac{1}{n}) since the interval ([1,0]) has a width of 1 andTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \right)  \left( \frac{(1)^3}{3}  \frac{(1)^4}{4} \rightTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x ) is (\frac{1}{n}) since the interval ([1,0]) has a width of 1 and is dividedTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \right)  \left( \frac{(1)^3}{3}  \frac{(1)^4}{4} \right)To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x ) is (\frac{1}{n}) since the interval ([1,0]) has a width of 1 and is divided intoTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \right)  \left( \frac{(1)^3}{3}  \frac{(1)^4}{4} \right) \To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x ) is (\frac{1}{n}) since the interval ([1,0]) has a width of 1 and is divided into (To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \right)  \left( \frac{(1)^3}{3}  \frac{(1)^4}{4} \right) ] To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x ) is (\frac{1}{n}) since the interval ([1,0]) has a width of 1 and is divided into (nTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \right)  \left( \frac{(1)^3}{3}  \frac{(1)^4}{4} \right) ] [To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x ) is (\frac{1}{n}) since the interval ([1,0]) has a width of 1 and is divided into (n)To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \right)  \left( \frac{(1)^3}{3}  \frac{(1)^4}{4} \right) ] [ =To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x ) is (\frac{1}{n}) since the interval ([1,0]) has a width of 1 and is divided into (n) equalTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \right)  \left( \frac{(1)^3}{3}  \frac{(1)^4}{4} \right) ] [ = To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x ) is (\frac{1}{n}) since the interval ([1,0]) has a width of 1 and is divided into (n) equal subTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \right)  \left( \frac{(1)^3}{3}  \frac{(1)^4}{4} \right) ] [ = 0To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x ) is (\frac{1}{n}) since the interval ([1,0]) has a width of 1 and is divided into (n) equal subintTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \right)  \left( \frac{(1)^3}{3}  \frac{(1)^4}{4} \right) ] [ = 0 To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x ) is (\frac{1}{n}) since the interval ([1,0]) has a width of 1 and is divided into (n) equal subintervalsTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \right)  \left( \frac{(1)^3}{3}  \frac{(1)^4}{4} \right) ] [ = 0  \To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x ) is (\frac{1}{n}) since the interval ([1,0]) has a width of 1 and is divided into (n) equal subintervals.
To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \right)  \left( \frac{(1)^3}{3}  \frac{(1)^4}{4} \right) ] [ = 0  \leftTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x ) is (\frac{1}{n}) since the interval ([1,0]) has a width of 1 and is divided into (n) equal subintervals.
ByTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \right)  \left( \frac{(1)^3}{3}  \frac{(1)^4}{4} \right) ] [ = 0  \left(To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x ) is (\frac{1}{n}) since the interval ([1,0]) has a width of 1 and is divided into (n) equal subintervals.
By evaluatingTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \right)  \left( \frac{(1)^3}{3}  \frac{(1)^4}{4} \right) ] [ = 0  \left( To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x ) is (\frac{1}{n}) since the interval ([1,0]) has a width of 1 and is divided into (n) equal subintervals.
By evaluating thisTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \right)  \left( \frac{(1)^3}{3}  \frac{(1)^4}{4} \right) ] [ = 0  \left( \To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x ) is (\frac{1}{n}) since the interval ([1,0]) has a width of 1 and is divided into (n) equal subintervals.
By evaluating this limitTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \right)  \left( \frac{(1)^3}{3}  \frac{(1)^4}{4} \right) ] [ = 0  \left( \fracTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x ) is (\frac{1}{n}) since the interval ([1,0]) has a width of 1 and is divided into (n) equal subintervals.
By evaluating this limit,To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \right)  \left( \frac{(1)^3}{3}  \frac{(1)^4}{4} \right) ] [ = 0  \left( \frac{To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x ) is (\frac{1}{n}) since the interval ([1,0]) has a width of 1 and is divided into (n) equal subintervals.
By evaluating this limit, youTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \right)  \left( \frac{(1)^3}{3}  \frac{(1)^4}{4} \right) ] [ = 0  \left( \frac{1To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x ) is (\frac{1}{n}) since the interval ([1,0]) has a width of 1 and is divided into (n) equal subintervals.
By evaluating this limit, you canTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \right)  \left( \frac{(1)^3}{3}  \frac{(1)^4}{4} \right) ] [ = 0  \left( \frac{1}{To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x ) is (\frac{1}{n}) since the interval ([1,0]) has a width of 1 and is divided into (n) equal subintervals.
By evaluating this limit, you can findTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \right)  \left( \frac{(1)^3}{3}  \frac{(1)^4}{4} \right) ] [ = 0  \left( \frac{1}{3To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x ) is (\frac{1}{n}) since the interval ([1,0]) has a width of 1 and is divided into (n) equal subintervals.
By evaluating this limit, you can find theTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \right)  \left( \frac{(1)^3}{3}  \frac{(1)^4}{4} \right) ] [ = 0  \left( \frac{1}{3}To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x ) is (\frac{1}{n}) since the interval ([1,0]) has a width of 1 and is divided into (n) equal subintervals.
By evaluating this limit, you can find the exactTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \right)  \left( \frac{(1)^3}{3}  \frac{(1)^4}{4} \right) ] [ = 0  \left( \frac{1}{3} To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x ) is (\frac{1}{n}) since the interval ([1,0]) has a width of 1 and is divided into (n) equal subintervals.
By evaluating this limit, you can find the exact areaTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \right)  \left( \frac{(1)^3}{3}  \frac{(1)^4}{4} \right) ] [ = 0  \left( \frac{1}{3}  \To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x ) is (\frac{1}{n}) since the interval ([1,0]) has a width of 1 and is divided into (n) equal subintervals.
By evaluating this limit, you can find the exact area ofTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \right)  \left( \frac{(1)^3}{3}  \frac{(1)^4}{4} \right) ] [ = 0  \left( \frac{1}{3}  \fracTo find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x ) is (\frac{1}{n}) since the interval ([1,0]) has a width of 1 and is divided into (n) equal subintervals.
By evaluating this limit, you can find the exact area of theTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \right)  \left( \frac{(1)^3}{3}  \frac{(1)^4}{4} \right) ] [ = 0  \left( \frac{1}{3}  \frac{To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x ) is (\frac{1}{n}) since the interval ([1,0]) has a width of 1 and is divided into (n) equal subintervals.
By evaluating this limit, you can find the exact area of the regionTo find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \right)  \left( \frac{(1)^3}{3}  \frac{(1)^4}{4} \right) ] [ = 0  \left( \frac{1}{3}  \frac{1To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x ) is (\frac{1}{n}) since the interval ([1,0]) has a width of 1 and is divided into (n) equal subintervals.
By evaluating this limit, you can find the exact area of the region.To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \right)  \left( \frac{(1)^3}{3}  \frac{(1)^4}{4} \right) ] [ = 0  \left( \frac{1}{3}  \frac{1}{4To find the area of the region between the graph (y = x^2  x^3) and the xaxis over the interval ([1,0]) using the limit process, you would follow these steps:

Split the region into infinitesimally small rectangles parallel to the xaxis.

Approximate the area of each rectangle by multiplying its width (which approaches zero) by the height of the function at some point within that rectangle.

Sum up the areas of all these rectangles to get an approximation of the total area.

Take the limit as the width of the rectangles approaches zero to get the exact area.
Mathematically, the area can be expressed as the integral of the function (y = x^2  x^3) over the interval ([1,0]):
[ \text{Area} = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x ]
where ( f(x_i) ) is the value of the function at some point within the (i)th subinterval, and ( \Delta x ) is the width of each subinterval. In this case, ( \Delta x ) is (\frac{1}{n}) since the interval ([1,0]) has a width of 1 and is divided into (n) equal subintervals.
By evaluating this limit, you can find the exact area of the region.To find the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) using the limit process, you would follow these steps:

Determine the definite integral of the function ( y = x^2  x^3 ) over the interval ([1, 0]), which represents the area under the curve between (1) and (0).

To set up the definite integral, integrate the function ( y = x^2  x^3 ) with respect to ( x ) over the interval ([1, 0]). This gives you the expression: (\int_{1}^{0} (x^2  x^3) , dx).

Evaluate the integral: [ \int_{1}^{0} (x^2  x^3) , dx = \left[ \frac{x^3}{3}  \frac{x^4}{4} \right]_{1}^{0} ] [ = \left( \frac{0^3}{3}  \frac{0^4}{4} \right)  \left( \frac{(1)^3}{3}  \frac{(1)^4}{4} \right) ] [ = 0  \left( \frac{1}{3}  \frac{1}{4} \right) ] [ = \frac{1}{3} + \frac{1}{4} ] [ = \frac{7}{12} ]

Therefore, the area of the region between the graph ( y = x^2  x^3 ) and the xaxis over the interval ([1, 0]) is ( \frac{7}{12} ) square units.
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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