Calculus (3rd Edition)

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

Chapter 7 - Exponential Functions - 7.8 Inverse Trigonometric Functions - Preliminary Questions - Page 374: 4


$$ b=\sqrt 3.$$

Work Step by Step

$$ \int_{0}^{b} \frac{d x}{1+x^{2}}=\frac{\pi}{3} \Longrightarrow \tan^{-1} x|_0^b=\frac{\pi}{3}\\ \tan^{-1} b- \tan^{-1}0=\frac{\pi}{3}\Longrightarrow \tan^{-1} b-0=\frac{\pi}{3} \\\Longrightarrow b=\sqrt 3. $$
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