University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 8 - Section 8.3 - Trigonometric Substitutions - Exercises - Page 439: 5



Work Step by Step

Let us consider $x =3 \sin \theta $ and $dx=3 \cos \theta d \theta $ Now, the given integral becomes: $\int \dfrac{3 \cos \theta d \theta }{\sqrt{9-9 \sin^2 \theta}} = \int d \theta$ Now, integrate with limits: $\int_{0}^{3/2} d \theta=[sin^{-1} (x/3)]_{0}^{3/2}=\dfrac{\pi}{6}$
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