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: 22



Work Step by Step

=$\int\int_R\frac{y}{x^2y^2+1}dA$ =$\int_{0}^{1}\int^{1}_{0}\frac{y}{(xy)^2+1}dx dy$ =$\int^{1}_{0}[tan^{-1}(xy)]^1_0dy$ =$\int^{1}_{0}tan^{-1}ydy$ =$[y tan^{-1}y-\frac{1}{2}ln|1+y^2|]$ =$\frac{\pi}{4}-\frac{1}{2}ln2$
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