Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 8: Techniques of Integration - Section 8.8 - Improper Integrals - Exercises 8.8 - Page 501: 1



Work Step by Step

Let $f(x)=\int_{0}^{\infty} \dfrac{1}{(x^2+1)} dx$ Now, $\lim\limits_{k \to \infty} f(x)= \lim\limits_{k \to \infty}\int_{0}^{k} \dfrac{1}{x^2+1} dx$ Thus, $\lim\limits_{k \to \infty} [\tan^{-1} x]_{0}^{k}=\lim\limits_{k \to \infty} [\tan^{-1} (k)-\tan^{-1} (0)]= \dfrac{\pi}{2}$
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