Answer
$$24.60296$$
Work Step by Step
\begin{aligned}
s &=\int_{a}^{b} \sqrt{x^{\prime}(t)^{2}+y^{\prime}(t)^{2}} d t \\
&=\int_{0}^{2\pi} \sqrt{ 25\sin^2 5t+9\cos^23t } d t \\
&\approx 24.60296
\end{aligned}
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 12 - Parametric Equations, Polar Coordinates, and Conic Sections - 12.2 Arc Length and Speed - Exercises - Page 611: 14
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