Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 8 - Techniques of Integration - Chapter Review Exercises - Page 461: 79


The integral converges and its value is $\pi/2$.

Work Step by Step

We have $$ \int_{-\infty}^{0} \frac{d x}{x^2+1}=\tan^{-1}x|_{-\infty}^0\\ =\tan^{-1}0-\tan^{-1}(-\infty)=0-(-\pi/2)=\pi/2. $$ Hence, the integral converges and its value is $\pi/2$.
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