Answer
$$\sin^{-1}\frac{2}{3}-\sin^{-1}\frac{1}{3}.$$
Work Step by Step
We have
$$\int_{1/3}^{2/3} \frac{1}{\sqrt{1-x^2}}dx =\sin^{-1}x|_{1/3}^{2/3}
= \sin^{-1}\frac{2}{3}-\sin^{-1}\frac{1}{3}.$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 7 - Exponential Functions - Chapter Review Exercises - Page 387: 75
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