## Calculus 10th Edition

$\frac{768\pi}{7}$
Setup the integration using shell method about the x-axis $2\pi \int_0^8 y(\sqrt[3] y) dy$ $2\pi \int_0^8 y^{\frac{4}{3}} dy$, Integrate $2\pi [\frac{3}{7}y^{\frac{7}{3}}]_0^8$, Take definite integral $\frac{768\pi}{7}$ Simplify