Thomas' Calculus 13th Edition

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

Chapter 15: Multiple Integrals - Section 15.1 - Double and Iterated Integrals over Rectangles - Exercises 15.1 - Page 875: 29



Work Step by Step

V=$\int\int f(x,y)dA$ =$\int^{\frac{\pi}{2}}_{0} \int^{\frac{\pi}{4}}_{0}2 \sin x \cos y dydx$ =$\int^{\frac{\pi}{2}}_{0}[2sinx siny]^\frac{\pi}{4}_0dx$ =$\int^{\frac{\pi}{2}}_{0}(\sqrt{2} \sin x)dx$ $ =[-\sqrt{2} \cos x]^\frac{\pi}{2}_0$ =$\sqrt{2}$
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