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 15.2 - Double Integrals over General Regions - Exercises 15.2 - Page 883: 69



Work Step by Step

Consider $I= \int_{1}^{\infty} \int_{e^{-x}}^{1} \dfrac{1}{x^3y} dy dx$ or, $= \int_{1}^{\infty}[\dfrac{\ln 1}{x^3}-\dfrac{\ln e^{-x}}{x^3}] dx$ or, $=\int_{1}^{\infty} 0-\dfrac{-x}{x^3} dx$ Thus, we have $I=[-x^{-1}]_1^{\infty} =0+1=1$
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