Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 15: Multiple Integrals - Practice Exercises - Page 933: 27



Work Step by Step

$$Volume=V=2 \int_0^{\pi/2} \int_{-\cos y}^{0} \int_{0}^{-2x} \ dz \ dx \ dy \\= \int_0^{\pi/2} \int_{-\cos y}^{0} (-2x) \times (2) \ dx \ dy \\=2 \int_0^{\pi/2} \cos^2 y \ dy \\=2 [\dfrac{y}{2} +\dfrac{1}{4} \times \sin 2y]_0^{\pi/2} \\=\dfrac{\pi}{2}$$
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