University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 6 - Practice Exercises - Page 391: 17


$ \dfrac{10}{3}$

Work Step by Step

Our aim is to integrate the integral in order to find the arc length. $$L= \int_{p}^{q} \sqrt {1+(y')^2}$$ $$ \\=\int_{1}^{4} \sqrt {1+\dfrac{1}{4} (\dfrac{1}{x} -2+x)} dx \\=0.5 [2\sqrt x +\dfrac{2x^{(3/2)}} {3}]_1^4 \\ = \dfrac{10}{3}$$
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