Answer
$\frac{256\pi}{15}$
Work Step by Step
Setup the integration using disk method about the x-axis
$\pi \int_0^2 (4-x^2)^2 dx$
$\pi \int_0^2(16 - 8x^2 +x^4)dx$, Integrate
$\pi [16x-\frac{8}{3}x^3 + \frac{1}{5}x^5 ] _0^2$, Evaluate the definite integral
$\pi(32-\frac{64}{3} + \frac{32}{5})$
$\pi(\frac{32}{3} + \frac{32}{5})$
$\frac{256\pi}{15}$
