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: 71



Work Step by Step

Consider $I= \int_{-\infty}^{\infty} \dfrac{dx}{x^2+1} \int_{-\infty}^{\infty} \dfrac{dy}{y^2+1}$ or, $=[ \arctan x]_{-\infty}^{\infty} [ \arctan y]_{-\infty}^{\infty}$ or, $=[\arctan x (-\infty) -\arctan x (\infty)] [\arctan y (-\infty) -\arctan y (\infty)] $ Thus, we have $I=\pi \cdot \pi =\pi^2$
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