Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 4 - Applications of the Derivative - Review Exercises: 73

Answer

$$\theta + \frac{1}{3}\sin 3\theta + C$$

Work Step by Step

$$\eqalign{ & \int {\left( {1 + \cos 3\theta } \right)} d\theta \cr & {\text{split the numerator}} \cr & = \int {d\theta } + \int {\cos 3\theta } d\theta \cr & {\text{integrate}}{\text{, use }}\int {\cos ax} dx = \frac{1}{a}\sin ax + C \cr & letting{\text{ }}a = 3,{\text{ }}\theta = x \cr & = \theta + \frac{1}{3}\left( {\sin 3\theta } \right) + C \cr & = \theta + \frac{1}{3}\sin 3\theta + C \cr} $$
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