How do you estimate the area under the graph of #f(x)=4sqrt(x)# from #x=0# to #x=4# using four approximating rectangles and right endpoints?
Find the value of
giving 4 subranges:
Use the mid point of each range as the rectangular height for the
Approximate area
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To estimate the area under the graph of ( f(x) = 4\sqrt{x} ) from ( x = 0 ) to ( x = 4 ) using four approximating rectangles and right endpoints, follow these steps:

Divide the interval ( [0, 4] ) into four equal subintervals. Since we have four rectangles, each subinterval will have a width of ( \Delta x = \frac{4}{4} = 1 ).

Choose the right endpoint of each subinterval as the height of the corresponding rectangle. Calculate the height of each rectangle by evaluating the function ( f(x) = 4\sqrt{x} ) at the right endpoint of each subinterval.

Calculate the area of each rectangle by multiplying its height by its width (( \Delta x = 1 )).

Sum up the areas of all four rectangles to estimate the total area under the graph.
The formula for the area of a rectangle is: ( \text{Area} = \text{height} \times \text{width} ).
So, the estimation of the area under the graph of ( f(x) = 4\sqrt{x} ) from ( x = 0 ) to ( x = 4 ) using four approximating rectangles and right endpoints is the sum of the areas of the four rectangles:
[ \text{Area} \approx 4\sqrt{1} \times 1 + 4\sqrt{2} \times 1 + 4\sqrt{3} \times 1 + 4\sqrt{4} \times 1 ]
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