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: 18

Answer

$\overline{x}=0$ and $\overline{y}=\dfrac{3}{3}=1$

Work Step by Step

We have a triangle has vertices $(-1,0), (1,0), (0,3)$, which is symmetric about the $y-axis$ and the center of mass has $x$-co-ordinate of $0$. Also, the y-coordinate is a third of the distance of $(0,3)$. Therefore, the center of mass is: $\overline{x}=0$ and $\overline{y}=\dfrac{3}{3}=1$
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