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: 20



Work Step by Step

$\int\int_R xy e^{xy^2}dA$ =$\int_0^2\int_0^1 xy e^{xy^2}dydx$ =$\int^{ln2}_{0}[\frac{1}{2}e^{xy^2}]^{ln2}_0$dx =$\int^{ln2}_{0}[-e^{x}]^{1}_0$dx =$\int^{2}_{0}(\frac{1}{2}e^x-\frac{1}{2})dx$ =$[\frac{1}{2}e^x-\frac{1}{2}x]^2_0$ =$\frac{1}{2}(e^2-3)$
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