Thomas' Calculus 13th Edition

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

Chapter 15: Multiple Integrals - Practice Exercises - Page 934: 45


$M=3 \delta$ $I_x=2 \delta$

Work Step by Step

$$M= \delta \int_{0}^{3} \int_{0}^{2x/3} \ dy \ dx \\= \delta \int_{0}^{3} \dfrac{2}{3} \times x \ dy \ dx \\= 3 \delta \\I_x= \delta \int_{0}^{3} \int_{0}^{2x/3} y^2 \ dy \ dx \\= \int_{0}^{3} \dfrac{8 x^3 \delta}{81} \ dx \\=(\dfrac{8 \delta}{81}) (\dfrac{3^4}{4})=2\delta $$
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