Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 7 - Principles Of Integral Evaluation - 7.4 Trigonometric Substitutions - Exercises Set 7.4: 27

Answer

True.

Work Step by Step

Using a substitution $x=asin\theta$ yields $$\sqrt{a^{2}-x^{2}}=\sqrt{a^{2}-a^{2}sin^{2}(\theta)}=\sqrt{a^{2}(1-sin^{2}(\theta))}=acos\theta$$ This simplifies the integral.
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