Answer
$\frac{\pi}{3}$
Work Step by Step
Setup the integration using Shell method
$ 2\pi \int_0^1 x(1-x) dx $
$2\pi \int_0^1 (x-x^2)dx$
$ 2\pi (\frac{1}{2}x^2 - \frac{1}{3}x^3)]_0^1 $, Integrate
$ 2\pi ((\frac{1}{2} - \frac{1}{3}) - 0)$ , Definite Integral taken
$\frac{\pi}{3}$
