University Calculus: Early Transcendentals (3rd Edition)

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

Chapter 6 - Section 6.6 - Moments and Centers of Mass - Exercises - Page 390: 26


$\dfrac{\delta}{54}(10\sqrt {10}-1)$

Work Step by Step

The formula to calculate the arc length is as follows: $L=\int_m^n \sqrt {1+[y']^2} dx$ Now, $m_x=\delta \int_0^1 (x^3) \sqrt {1+9x^4} dx$ Suppose $a= 1+9x^4$ So, $=\dfrac{\delta}{36} \int_{1}^{10} a^{1/2} da$ or, $=\dfrac{\delta}{54}(10\sqrt {10}-1)$
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