Answer
$\frac{128\pi}{15}$
Work Step by Step
Set up the radius using the washer method
$2\pi\int_0^2(x\sqrt(4-x^2))^2-0 dx$
The 2 before the $\pi$ indicates the symmetry in the graph(Check graph below)
$2\pi\int_0^2(x^2(4-x^2))dx$
$2\pi\int_0^2(4x^2-x^4)dx$
$2\pi[\frac{4x^3}{3} - \frac{x^5}{5}]_0^2$
Now solve:
$2\pi[\frac{32}{3} - \frac{32}{5}]$
= $\frac{128\pi}{15}$
