Calculus (3rd Edition)

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

Chapter 8 - Techniques of Integration - 8.4 Integrals Involving Hyperbolic and Inverse Hyperbolic Functions - Exercises - Page 415: 28



Work Step by Step

\begin{aligned} \int_{0.2}^{0.8} \frac{1}{x \sqrt{1-x^{2}}} d x &=\left[-\operatorname{sech}^{-1} x\right]_{0.2}^{0.8} \\ &=-\operatorname{sech}^{-1}(0.8)-\left[-\operatorname{sech}^{-1}(0.2)\right] \\ &=\operatorname{sech}^{-1}(0.2)-\operatorname{sech}^{-1}(0.8) \end{aligned}
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