Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 6 - Section 6.3 - Volumes by Cylindrical Shells - 6.3 Exercises - Page 454: 23


b.) $\displaystyle{V=4\pi\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\pi\cos^4x-x\cos^4x\ dx}\\ $ b.) $\displaystyle{V=46.50942}$

Work Step by Step

a.) $\displaystyle{V=\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\left(2\pi\left(\pi-x\right)\right)\left(\cos^4x-\left(-\cos^4x\right)\right)\ dx}\\ \displaystyle{V=\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\left(2\pi\left(\pi-x\right)\right)\left(2\cos^4x\right)\ dx}\\ \displaystyle{V=4\pi\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\pi\cos^4x-x\cos^4x\ dx}\\ $ b.) $\displaystyle{V=46.50942}$
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