Thomas' Calculus 13th Edition

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

Chapter 15: Multiple Integrals - Section 15.6 - Moments and Centers of Mass - Exercises 15.6 - Page 908: 2


$$ M=9 \delta, \ \ I_x= 27 \delta, \ \ I_y=27 \delta$$

Work Step by Step

Since \begin{align*} M&=\delta \int_{0}^{3} \int_{0}^{3} d y d x\\ &=\delta \int_{0}^{3} 3 d x\\ &=9 \delta \end{align*} and \begin{align*} I_{x}&=\delta \int_{0}^{3} \int_{0}^{3} y^{2} d y d x\\ &=\delta \int_{0}^{3}\left[\frac{y^{3}}{3}\right]_{0}^{3} d x\\ &=27 \delta \end{align*} and \begin{align*} I_{y}&=\delta \int_{0}^{3} \int_{0}^{3} x^{2} d y d x\\ &=\delta \int_{0}^{3}\left[x^{2} y\right]_{0}^{3} d x\\ &=\delta \int_{0}^{3} 3 x^{2} d x\\ &=27 \delta \end{align*}
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.