Chapter 6 - Section 6.3 - Volumes by Cylindrical Shells - 6.3 Exercises - Page 454: 4

$\displaystyle{V=\frac{62\pi}{5}}$

$\displaystyle{V=\int_{1}^{2}(2\pi x)\left(x^3\right)\ dx}\\ \displaystyle{V=2\pi\int_{1}^{2}x^{4}\ dx}\\ \displaystyle{V=2\pi\left[\frac{1}{5}x^{5}\right]_{1}^{2}}\\ \displaystyle{V=2\pi\left(\left(\frac{1}{5}(2)^{5}\right)-\left(\frac{1}{5}(1)^{5}\right)\right)}\\ \displaystyle{V=\frac{62\pi}{5}}$