Calculus: Early Transcendentals 8th Edition

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

Chapter 6 - Review - Exercises - Page 466: 12


$ 2 \pi \int _{0}^{\frac{ \pi }{3}}x \left( tanx-x \right) dx $

Work Step by Step

{Step 1 of 2} Consider the region enclosed by the graphs of $ y=tanx $, $ y=x $ and $ x=\frac{ \pi }{3}. $ {Step 2 of 2} We use the method of cylindrical shells.A typical shell is shown above.The radius of the shell is r(x)=x and the height of the shell is $ h \left( x \right) =tanx-x $ . The volume V of the resulting solid of revolution is given by $ V=2 \pi \int _{0}^{\frac{ \pi }{3}}r \left( x \right) h \left( x \right) dx $ $ =2 \pi \int _{0}^{\frac{ \pi }{3}}x \left( tanx-x \right) dx $
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