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 15.2 - Double Integrals over General Regions - Exercises 15.2 - Page 883: 58



Work Step by Step

Consider $V= \int_{-2}^{1} \int_{x}^{2-x^2} x^2 dy dx$ or, $= \int_{-2}^{1} [x^2 y]_{x}^{2-x^2} dx$ or, $= \int_{-2}^{1} 2x^2-x^4-x^3 dx$ or, $= [ \dfrac{2x^3}{3}-\dfrac{x^5}{5}-\dfrac{x^4}{4}]_{-2}^{1}$ Thus, we have $I= [ \dfrac{2}{3}-\dfrac{1}{5}-\dfrac{1}{4}]- [ \dfrac{-16}{3}+\dfrac{32}{5}-\dfrac{16}{4}]=\dfrac{63}{20}$
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.