Try the fastest way to create flashcards

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. y=cos 2x, y=0, x=0, x=π/4


Answered 9 months ago
Answered 9 months ago
Step 1
1 of 2

To find the Volume\textbf{Volume} of the solid given we will apply The Disk Method\textbf{The Disk Method} ...


From the exercise given we can see that we need to find

V=π0π/4(cos(2x))2dx\begin{equation} V=\pi\int_{0}^{\pi/4}{(\cos{(2x)})^2dx} \end{equation}

This leads\textbf{This leads} to:

V=π0π/4cos(4x)12dx=π20π/4(cos(4x)1)dx=π2[sin(4x)4+x]0π/4=π28\begin{align*} V&=\pi\int_{0}^{\pi/4}{\frac{\cos{(4x)}-1}{2}dx}\\ &=\frac{\pi}{2}\int_{0}^{\pi/4}{(\cos{(4x)}-1)dx}\\ &=\frac{\pi}{2}\left[\frac{\sin{(4x)}}{4}+x\right]_{0}^{\pi/4}\\ &=\frac{\pi^2}{8}\\ \end{align*}

So, our final answer\textbf{final answer} is:


Create a free account to view solutions

Create a free account to view solutions

Recommended textbook solutions

Thomas' Calculus 14th Edition by Christopher E Heil, Joel R. Hass, Maurice D. Weir

Thomas' Calculus

14th EditionISBN: 9780134438986 (11 more)Christopher E Heil, Joel R. Hass, Maurice D. Weir
10,142 solutions
Calculus 10th Edition by Bruce H. Edwards, Ron Larson


10th EditionISBN: 9781285057095 (6 more)Bruce H. Edwards, Ron Larson
12,387 solutions
Calculus: Early Transcendentals 8th Edition by James Stewart

Calculus: Early Transcendentals

8th EditionISBN: 9781285741550 (6 more)James Stewart
11,085 solutions
Calculus: Early Transcendentals 9th Edition by Daniel K. Clegg, James Stewart, Saleem Watson

Calculus: Early Transcendentals

9th EditionISBN: 9781337613927 (1 more)Daniel K. Clegg, James Stewart, Saleem Watson
11,050 solutions

More related questions