University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 8 - Section 8.7 - Improper Integrals - Exercises - Page 471: 1


$ \dfrac{\pi}{2}$

Work Step by Step

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