Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 8 - Further Applications of Integration - 8.2 Area of a Surface of Revolution - 8.2 Exercises: 38


$S_g = S_f + 2\pi cL$

Work Step by Step

$g(x) = f(x) + c$ and $g'(x) = f'(x)$ $S_g = \int ^{b}_{a} 2\pi g(x) \sqrt{1+[g'(x)]^{2}}dx = \int^{b}_{a} 2\pi [f(x) + c] \sqrt{1+[f'(x)]^{2}}dx$ $ = \int ^{b}_{a} 2\pi f(x) \sqrt{1+[f'(x)]^{2}}dx + 2\pi c\int^{b}_{a} \sqrt{1+[f'(x)]^{2}}dx = S_f + 2\pi cL$
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