Answer
$2\pi.$
Work Step by Step
The volume is given by
$$
\pi\int_{\pi/4}^{3\pi/4} \csc^2x d x=\pi \left.\cot x\right|_{\pi/4}^{3\pi/4}=2\pi.
$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 6 - Applications of the Integral - 6.3 Volumes of Revolution - Exercises - Page 304: 11
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