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: 1

Answer

(a) i)$ \int ^{\frac{\pi}{3}}_{0} 2\pi \tan x \sqrt{1+\sec^{4}x}dx$ ii) $ \int^{\frac{\pi}{3}}_{0}2\pi x \sqrt{1+\sec^{4} x} dx$ (b) i) 10.5017 ii) 7.9353

Work Step by Step

(a) i) $y = \tan x$ then $dy/dx = \sec^{2} x$ and $ds = \sqrt{1+(dy/dx)^{2}}dx = \sqrt{1+\sec^{4} x}dx$ $S = \int 2\pi y ds = \int ^{\frac{\pi}{3}}_{0} 2\pi \tan x \sqrt{1+\sec^{4}x}dx$ ii) $S = \int 2\pi x ds = \int^{\frac{\pi}{3}}_{0}2\pi x \sqrt{1+\sec^{4} x} dx$ (b) i) 10.5017 ii) 7.9353
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