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How do you find the area between #y=x^2# and #y=8x#?

Answer 1

Area#=8^3/6#

Firstly we have to find the intersection between them. Let' solve the system of equation #y=x^2# and #y=8x# we have #x^2=8x# so that there are two solution #x=0# and #x=8#

the sought are is #int_0^8(8x-x^2)dx=8x^2/2-x^3/3|_0^8=8^3/2-8^3/3=8^3/6#

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Answer 2

Samantha Adkison

To find the area between the curves (y = x^2) and (y = 8x), you need to first determine the points where the curves intersect. Set (x^2 = 8x) and solve for (x) to find the intersection points. Once you have the intersection points, integrate the absolute difference between the two curves with respect to (x) over the interval where the curves overlap. The integral expression for finding the area would be (\int_{a}^{b} |f(x) - g(x)| , dx), where (f(x)) and (g(x)) represent the functions (y = x^2) and (y = 8x), respectively, and (a) and (b) are the x-values of the intersection points.

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Answer from HIX Tutor

When evaluating a one-sided 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.