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area between the curves y=4-x^2 and y=x-8
10 years ago

Answers

Steve
The curves intersect at (-4,-12) and (3,-5)

So, the area is just the sum of all the tiny rectangles with width dx, and height the distance between the curves:

A = ∫[-4,3] (4-x^2)-(x-8) dx
= ∫[-4,3] -x^2-x+12 dx
= -1/3 x^3 - 1/2 x^2 + 12x [-4,3]
= 343/6
10 years ago

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