Calculus (3rd Edition)

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

Chapter 8 - Techniques of Integration - 8.2 Trigonometric Integrals - Exercises - Page 403: 57



Work Step by Step

\begin{align*} \int_{-\pi/4}^{\pi/4} \sec^4 xdx&= \int_{-\pi/4}^{\pi/4} \sec^2 x\sec^2 xdx\\ &= \int_{-\pi/4}^{\pi/4} (1+\tan ^2 x)\sec^2 xdx\\ &=\tan x+\frac{1}{3}\tan^3x\bigg|_{-\pi/4}^{\pi/4}\\ & = \frac{8}{3} \end{align*}
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