University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 6 - Section 6.1 - Volumes Using Cross-Sections - Exercises - Page 356: 19


$$\dfrac{ 32 \pi}{5} $$

Work Step by Step

We need to integrate the integral to compute the volume. $$Volume = \int_{0}^{\pi/2} \pi x^4 \space dx \\=\dfrac{(\pi) x^5}{5}]_0^2 \\=(\pi)(\dfrac{(2^5)}{5}-0) \\= (\dfrac{\pi}{8})[\dfrac{\pi}{2}-0] \\=\dfrac{ 32 \pi}{5} $$
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