Answer
$\frac{21 \pi}{64}$
Work Step by Step
The volume is given by
$$
\pi \int_{1}^{4}\left(x^{-2}\right)^{2} d x=\pi \int_{1}^{4} x^{-4} d x=-\frac{\pi}{3} x^{-3}|_{1} ^{4}=\frac{21 \pi}{64}.
$$
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: 6
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