Solve the problem.
-Find the volume generated by revolving the curve $y = \cos 5 x$ about the $x$-axis, $0 \leq x \leq \pi / 60$
A) $\frac { \pi ^ { 2 } } { 120 } + \frac { \pi } { 60 }$
B) $\frac { \pi ^ { 2 } } { 120 }$
C) $\frac { \pi ^ { 2 } } { 120 } + \frac { \pi } { 40 }$
D) $\frac { \pi } { 120 } + \frac { 1 } { 40 }$

Question

Quizplus · Accepted Answer

We can use the formula $V=\int_{a}^{b}\pi y^{2}\,dx$ to find the volume of revolution. Plugging in $y=\cos5x$, we get $V=\int_{0}^{\pi/60}\pi\cos^{2}5x\,dx$. Using the identity $\cos2u=\cos^{2}u-\sin^{2}u$, we can rewrite $\cos^{2}5x=\frac{1}{2}(\cos10x+1)$. Plugging this in, we get $V=\frac{\pi}{20}\int_{0}^{\pi/60} \cos10x+1\,dx$. Evaluating the integral and simplifying, we get $V=\frac{\pi^{2}}{120}+\frac{\pi}{40}$. Therefore, the answer is choice C.

Solve the Problem y=cos⁡5xy = \cos 5 xy=cos5x About The xxx -Axis 0≤x≤π/600 \leq x \leq \pi / 600≤x≤π/60

Solve the Problem $y = \cos 5 x$ About The $x$ -Axis $0 \leq x \leq \pi / 60$