Multivariable Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 0-53849-787-4
ISBN 13: 978-0-53849-787-9

Chapter 10 - Parametric Equations and Polar Coordinates - Review - Exercises - Page 710: 38

Answer

$sinh 3$

Work Step by Step

$x=2+3t$, $y=cosh3t$ on $0\leq t\leq 1$ $x'=3$, $y'=3 sinh (3t)$ on $0\leq t\leq 2$ Length of the curve is given as: $L=\int_{0}^{1}\sqrt {(3)^2+(3 sinh (3t))^2} dt$ $=\int_{0}^{1} 3 (cosh 3t )dt$ $=sinh 3-sinh 0$ $=sinh 3$
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