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: 4

Answer

$$\frac{5\sqrt{5}-1}{2}$$

Work Step by Step

\begin{align*} s&=\int_{a}^{b} \sqrt{x^{\prime}(t)^{2}+y^{\prime}(t)^{2}} d t\\ &=\int_{0}^{1} \sqrt{9+36 t} d t\\ &= \frac{1}{36}\int_{0}^{1} 36\sqrt{9+36 t} d t\\ &=\frac{1}{36} \frac{2}{3}(9+36 t)^{3/2}\bigg|_{0}^{1}\\ &=\frac{5\sqrt{5}-1}{2} \end{align*}
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