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: 21

Answer

2 $ ln $ 2

Work Step by Step

We solve the double integral as follows: $\int\int_R\frac{xy^3}{s^2+1}dA $ =$\int_{0}^{1}\int^{2}_{0}\frac{xy^3}{s^2+1}dy dx $ =$\int^{1}_{0}[\frac{xy^4}{4(s^2+1)}]_0^2$ =$\int^{1}_{0}\frac{4x}{x^2+1}dx $ =$[2 ln|x^2+1|]^1_0$ =2 $ ln $ 2
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