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