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: 17

Answer

$\dfrac {5\pi }{32}\approx 0.49$

Work Step by Step

If $n$ is even $$\Rightarrow \int ^{\pi /2}_{0}\cos ^{n}xdx=\left( \dfrac {1}{2}\right) \left( \dfrac {3}{4}\right) \left( \dfrac {5}{6}\right) \ldots \left( \dfrac {n-1}{n}\right) \left( \dfrac {\pi }{2}\right) $$ $$\Rightarrow \int ^{\pi /2}_{0}\cos ^{6}xdx=\left( \dfrac {1}{2}\right) \left( \dfrac {3}{4}\right) \left( \dfrac {5}{6}\right) \left( \dfrac {\pi }{2}\right) =\dfrac {5\pi }{32}\approx 0.49$$
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