Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 8: Techniques of Integration - Practice Exercises - Page 518: 43


$$4 \sqrt{2}\left|\sin \frac{t}{4}\right|+C $$

Work Step by Step

We integrate as follows: \begin{align*} \int \sqrt{1+\cos \left(\frac{t}{2}\right)} d t&=\int \sqrt{2}\left|\cos \frac{t}{4}\right| d t\\ &=4 \sqrt{2}\left|\sin \frac{t}{4}\right|+C \end{align*}
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