Calculus: Early Transcendentals 8th Edition

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

Chapter 8 - Section 8.1 - Arc Length - 8.1 Exercises: 1

Answer

$4\sqrt(5)$

Work Step by Step

$y=2x-5$ $x=[-1,3]$ Equation y and its parameters are defined here y'=2dx Take the derivative of the equation given $L=\int_{-1}^{3}\sqrt (1+(f'(x))^{2})dx$ Plug the upper and lower limits into to equation for arc length $L=\int_{-1}^{3}\sqrt(1+(2)^2) dx$ Plug in the derivative of the original equation for f'(x) $L=\int_{-1}^{3}\sqrt(5) dx$ $L=\sqrt(5)x|_{-1}^{3}$ Plug in upper and lower bounds $L=3\sqrt(5)-(-\sqrt(5))$ Simplify $L=4\sqrt(5)$
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