Question

Set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.

y = sqrt(x), y = x^2; about y = 2
or $y = \sqrt{x}, y = x^2$; about $y = 2$

Answer 1

A washer has outer radius $2-x^2$ and inner radius $2 - \sqrt{x}$

$\displaystyle V = \int_0^1 \pi\Big[ \left( 2 - x^2 \right)^2 - \left( 2 - \sqrt{x}\right)^2\Big] dx$