University Calculus: Early Transcendentals (3rd Edition)

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

Chapter 6 - Section 6.3 - Arc Length - Exercises - Page 370: 14


$\dfrac{7 \sqrt 3}{3}$

Work Step by Step

The formula to calculate the arc length is as follows: $L=\int_{c}^{d} \sqrt {1+[f'(x)]^2} dx$ Re-write the equation as follows: $L=\int_{-2}^{-1} \sqrt {3x^4} dx$ Separate the terms and integrate as follows: $L= \sqrt 3 \int_{-2}^{-1} x^2 dx \\= \sqrt 3 (\dfrac{x^3}{3})_{-2}^{-1} \\= \dfrac{7 \sqrt 3}{3}$
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