## Calculus 10th Edition

$\frac{16\pi}{3}$
Setup the integration using shell method about the y-axis. Setup the integration using Shell Method $2\pi \int_0^2 x((4x-x^2) - x^2)dx$ $2 \pi \int_0^2 (4x^2 - 2x^3)dx$ ,Bring a factor of 2 out $4\pi \int_0^2 (2x^2 - x^3)dx$ $4\pi (\frac{2}{3} x^3 - \frac{1}{4} x^4)]_0^2$, Integrate $4\pi ( \frac{16}{3} -4) -0$, Take Definite Integral $\frac{16\pi}{3}$