Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 6: Applications of Definite Integrals - Section 6.6 - Moments and Centers of Mass - Exercises 6.6 - Page 361: 20


$\overline{x}=\dfrac{a}{3}$ and $\overline{y}=\dfrac{a}{3}$

Work Step by Step

We have a triangle with vertices $(0,0), (a,0), (0,a)$ whose x-coordinate corresponds to a third of the distance $(a,0)$ from the edge at the $y$-axis. Also, the y-coordinate is a third of the distance of $(0,a)$, which corresponds to the $x$-axis. Therefore, the center of mass is: $\overline{x}=\dfrac{a}{3}$ and $\overline{y}=\dfrac{a}{3}$
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