Calculus (3rd Edition)

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 610: 3



Work Step by Step

\begin{aligned} s &=\int_{a}^{b} \sqrt{x^{\prime}(t)^{2}+y^{\prime}(t)^{2}} d t \\ &=\int_{0}^{4} \sqrt{16 t^{2}+36 t^{2}} d t \\ &=\int_{0}^{4} \sqrt{52 t^{2}} d t \\ &=\int_{0}^{4} 2 \sqrt{13} t d t \\ &=\left.2 \sqrt{13} \cdot \frac{t^{2}}{2}\right|_{0} ^{4}\\ &=16\sqrt{13} \end{aligned}
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