Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the $x$-axis.
$$y = \cos x + 1 , x = 0 , y = 0 , x = \frac { 1 } { 2 } \pi$$
A) $\frac { 3 } { 4 } \pi ^ { 2 } + 2 \pi$
B) $\frac { 3 } { 4 } \pi ^ { 2 } + 4 \pi$
C) $\pi ^ { 2 } + 4 \pi$
D) $\pi ^ { 2 } + 2 \pi$

Question

Quizplus · Accepted Answer

The volume of the solid is calculated using the disk method: $ V = \pi \int_{0}^{\frac{\pi}{2}} (\cos x + 1)^2 \, dx $. Evaluating this integral gives $\frac{3}{4} \pi^2 + 2\pi$.

Find the Volume of the Solid Generated by Revolving the Region