# How do you find the volume of the solid obtained by rotating the region bounded by y=x and y=x^2 about the line x=-1?

$V = 2 \pi {\int}_{0}^{1} \left(x + 1\right) \left(x - {x}^{2}\right) \mathrm{dx} = 2 \pi {\int}_{0}^{1} \left(x - {x}^{3}\right) \mathrm{dx}$
$= 2 \pi {\left[{x}^{2} / 2 - {x}^{4} / 4\right]}_{0}^{1} = 2 \pi \left(\frac{1}{2} - \frac{1}{4}\right) = \frac{\pi}{2}$