Calculus (3rd Edition)

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

Chapter 7 - Exponential Functions - 7.9 Hyperbolic Functions - Exercises - Page 384: 58


$$ \sinh^{-1}(1)$$

Work Step by Step

Since $$\frac{d}{dx}\sinh^{-1}x=\frac{1}{\sqrt{1+x^2}}$$ Then \begin{align*} \int_{0}^{1} \frac{1}{\sqrt{1+x^{2}}} d x&= \sinh^{-1}x\bigg|_{0}^{1}\\ &= \sinh^{-1}(1)- \sinh^{-1}(0)\\ &= \sinh^{-1}(1) \end{align*}
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.