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: 44


$$\frac{1}{2}\left(\frac{1}{2}\sin 2x+\frac{1}{10}\sin 10x \right) +c$$

Work Step by Step

Using $$\cos (a x) \cos (b x)=\frac{1}{2} \cos ((a-b) x)+\frac{1}{2} \cos ((a+b) x)$$ We get \begin{align*} \int \cos 4x\cos 6 xdx&= \frac{1}{2} \int [\cos (-2 x)+ \cos (10x) ]dx\\ &=\frac{1}{2}\left(\frac{1}{2}\sin 2x+\frac{1}{10}\sin 10x \right) +c \end{align*}
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