Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 8 - Techniques of Integration - Chapter Review Exercises - Page 460: 63


$$ \frac{\pi}{3}$$

Work Step by Step

Given $$\int_{0}^{3 \sqrt{3} / 2} \frac{d x}{\sqrt{9-x^{2}}}$$ Then \begin{aligned} \int_{0}^{\frac{3 \sqrt{3}}{2}} \frac{d x}{\sqrt{9-x^{2}}} &=\int_{0}^{\frac{3 \sqrt{3}}{2}} \frac{d x}{\sqrt{9\left(1-(x / 3)^{2}\right)}} \\ &=\int_{0}^{\frac{3 \sqrt{3}}{2}} \frac{d x}{3 \sqrt{\left(1-(x / 3)^{2}\right)}} \\ &=\left.\sin ^{-1}\left(\frac{x}{3}\right)\right|_{0} ^{\frac{3 \sqrt{3}}{2}}\\ &= \frac{\pi}{3} \end{aligned}
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