# How do you find the volume of the solid obtained

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?
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Jayce Bates
By Shell Method,
$V=2\pi {\int }_{0}^{1}\left(x+1\right)\left(x-{x}^{2}\right)dx=2\pi {\int }_{0}^{1}\left(x-{x}^{3}\right)dx$
$=2\pi \left[\frac{{x}^{2}}{2}-\frac{{x}^{4}}{4}{\right]}_{0}^{1}=2\pi \left(\frac{1}{2}-\frac{1}{4}\right)=\frac{\pi }{2}$