Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 9 - Further Applications of the Integral and Taylor Polynomials - 9.1 Arc Length and Surface Area - Exercises - Page 468: 7



Work Step by Step

Given $$y=x^{3/2}$$ The arc length given by \begin{aligned} \int_{a}^{b} \sqrt{1+\left(y^{\prime}\right)^{2}} d x &=\int_{1}^{2} \sqrt{1+\left(\frac{3}{2} x^{1 / 2}\right)^{2}} d x \\ &=\int_{1}^{2} \sqrt{1+\frac{9}{4}} x d x \\ &=\frac{2}{3}\frac{4}{9}\left(1+\frac{9}{4}\right)^{3/2}\bigg|_{1}^{2}\\ &= \frac{22\sqrt{22}-13\sqrt{13}}{27} \end{aligned}
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