Calculus 8th Edition

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

Chapter 8 - Further Applications of Integration - Review - Concept Check - Page 621: 2


a) See the explanation below. b) See the explanation below. c) See the explanation below.

Work Step by Step

a) Let the surface area of the curve $C$ be $S$ about the $x$-axis. Such as: $S=\int_a^b2 \pi f(x) \sqrt {1+[f'(x)]^2} dx$ b) Formula to calculate the surface area of the curve $C$ be $S$ about the $x$-axis given when $x$ can be given as function of $y$ as: $S=\int_c^d2 \pi f(y) \sqrt {1+[g'(y)]^2} dy$ c) From part (a) and (b), we have $S=\int_a^b2 \pi f(x) \sqrt {1+[f'(x)]^2} dx$; for $y=f(x)$ and $S=\int_c^d2 \pi f(y) \sqrt {1+[g'(y)]^2} dy$ for $x$ as a function of $y$
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