Answer
$\frac{8\pi}{3}$
Work Step by Step
Setup the integration using shell method about the y-axis
$ 2\pi \int_0^2 x(4-(4x-x^2))dx$
$ 2\pi \int_0^2 (4x-4x^2 +x^3)dx$, Integrate
$2\pi (2x^2 - \frac{4}{3}x^3 + \frac{1}{4}x^4)]_0^2 $, Take the definite integral
$2\pi(8-\frac{32}{3} +4)-0$
$\frac{8\pi}{3}$
