Question :

Find the volume of the solid generated if the region bounded by the curve $\displaystyle y=x^2$ , $\displaystyle x=1$ is revolved about $\displaystyle x=0$.

Attempt:

I drew the figure and got ;

$\displaystyle V=2\pi r h t$

$\displaystyle 2\pi [\frac{x^3}{3}-\frac{x^4}{4}]\int $-limit from 1 to 0

= $\displaystyle \frac{\pi}{6}$