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