# Calculus: Application of Integration

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Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle and label ts height and width. Then find the area of the region.

y=x^2
y^2=x

• Calculus: Application of Integration -

It is easy to see that the two curves intersect at (0,0) and (1,1)
I will integrate with respect to x
area = [integral] (x^(1/2) - x^2) dx from 0 to 1
= [(2/3)x^(3/2) - (1/3)x^3] from 0 to 1
= 2/3 - 1/3 - 0
= 1/3

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