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 generated by revolving the region around the x-axis can be found using the disk method. The formula for the volume is $V = \pi \int_{a}^{b} [f(x)]^2 dx$, where $f(x) = \cos(x) + 1$, $a = 0$, and $b = \frac{1}{2}\pi$. Calculating this integral gives $\frac{3}{4}\pi^2 + 2\pi$, which matches option A.

Find the Volume of the Solid Generated by Revolving the Region