Answer
$$\dfrac{128 \pi}{7} $$
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} $$
University Calculus: Early Transcendentals (3rd Edition)
by Hass, Joel R.; Weir, Maurice D.; Thomas Jr., George B.
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
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