Calculus (3rd Edition)

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

Chapter 7 - Exponential Functions - Chapter Review Exercises - Page 387: 77


$$\frac{\sinh 2}{2}.$$

Work Step by Step

Let $ u=2t $, then $ du=2dt $, $ t:=0\to 1, u:=0\to 2$. Now, we have $$\int_0^1\cosh (2t) dt =\frac{1}{2}\int_0^2\cosh u du \\ =\frac{1}{2} \sinh u|_0^2=\frac{1}{2}(\sinh 2-\sinh 0)= \frac{\sinh 2}{2}.$$
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