Answer
$$V=\frac{6\pi}{55}$$
Work Step by Step
$V=\pi\int_0^1 (x^2)^2-(x^5)^2dx$
$V=\pi\int_0^1 (x^4-x^{10}) dx$
$V=\pi[\frac{x^5}{5}-\frac{x^{11}}{11}]_0^1$
$V=\pi [(\frac{1^5}{5}-\frac{1^{11}}{11})-(\frac{0^5}{5}-\frac{0^{11}}{11})]$
$V=\pi[(\frac{1}{5}-\frac{1}{11})-(0)]$
$V=\pi(\frac{11}{55}-\frac{5}{55})$
$V=\frac{6\pi}{55}$
