University Calculus: Early Transcendentals (3rd Edition)

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

Chapter 14 - Section 14.7 - Triple Integrals in Cylindrical and Spherical Coordinates - Exercises - Page 805: 55



Work Step by Step

Our aim is to integrate the integral as follows: $$ Volume=8\int^{\pi/2}_0 \int^\sqrt{2}_1 \int^r_0 dz r dr \space d\theta \\=(8) \int^{\pi/2}_0 \int^{\sqrt{2}}_1 r^2 \space dr \space d\theta\\=(8) \times (\dfrac{2\sqrt{2}-1}{3}) \times \int^{\pi/2}_0 (1) d\theta \\=\dfrac{4\pi(2\sqrt{2}-1)}{3}$$
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