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: 6



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 t^{4}+4 t^{2}} d t\\ &=\int_{0}^{1} \sqrt{t^{2}\left(9 t^{2}+4\right)} d t\\ &=\frac{1}{18} \int_{0}^{1} 18 t\left(9 t^{2}+4\right)^{1 / 2} d t\\ &=\left.\frac{1}{18} \frac{\left(9 t^{2}+4\right)^{3 / 2}}{3 / 2}\right|_{0} ^{1}\\ &=\frac{13\sqrt{13}-8}{27} \end{align*}
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