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: 20


$$\dfrac{128 \pi}{7} $$

Work Step by Step

We need to integrate the integral to compute the volume. $Volume= \int_{0}^{\pi/2} \pi x^6 \space dx \\=(\pi)\times [\dfrac{x^7}{7}]_0^2 \\ =\dfrac{2^7(\pi)}{7}-0 \\=\dfrac{128 \pi}{7} $$
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