Volumes for Two Functions

If the region bounded by the upper function $y_{upper}=f(x)$ and the lower funciton $y_{lower}=g(x)$, and the lines $x=a$ and $x=b$ is revolved about the $x$-axis, then its volume of revolution is given by: $$ \begin{align} \displaystyle V &= \int_{a}^{b}{\Big([f(x)]^2 - [g(x)]^2\Big)}dx \\ &= \int_{a}^{b}{\Big(y_{upper}^2 - y_{lower}^2\Big)}dx \end{align} $$

Example 1

Find the volume of revolution generated by revolving the region between $y=x^2$ and $y=\sqrt{x}$ about the $x$-axis.