Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 8 - Integration Techniques, L'Hopital's Rule, and Improper Integrals - 8.3 Exercises: 14

Answer

$\dfrac {128}{315}\approx 0.406$

Work Step by Step

If $n$ is odd $(n\geq3)$ $$\Rightarrow \int ^{\pi /2}_{0}\cos ^{n}xdx=\left( \dfrac {2}{3}\right) \left( \dfrac {4}{5}\right) \left( \dfrac {6}{7}\right) \ldots \left( \dfrac {n-1}{n}\right) $$ $$\Rightarrow \int ^{\pi /2}_{0}\cos ^{9}xdx=\left( \dfrac {2}{3}\right) \left( \dfrac {4}{5}\right) \left( \dfrac {6}{7}\right) \left( \dfrac {8}{9}\right) =\dfrac {128}{315}\approx 0.406$$
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