Answer
b.) $\displaystyle{V=4\pi\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\pi\cos^4x-x\cos^4x\ dx}\\ $
b.) $\displaystyle{V=46.50942}$
Work Step by Step
a.)
$\displaystyle{V=\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\left(2\pi\left(\pi-x\right)\right)\left(\cos^4x-\left(-\cos^4x\right)\right)\ dx}\\
\displaystyle{V=\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\left(2\pi\left(\pi-x\right)\right)\left(2\cos^4x\right)\ dx}\\
\displaystyle{V=4\pi\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\pi\cos^4x-x\cos^4x\ dx}\\ $
b.)
$\displaystyle{V=46.50942}$
