Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 15 - Multiple Integrals - 15.6 Triple Integrals - 15.6 Exercises - Page 1077: 12



Work Step by Step

Let us consider that $I=\iiint_E \sin y dV$ $ I=\int_{0}^{\pi} \int_{0}^{\pi-x} \int_{0}^{x}\sin y dzdy dx$ Further, we have $\int_{0}^{\pi} [-x (\cos y)]_{0}^{\pi-x} dx=\int_{0}^{\pi} [x (\cos x)+x] dx$ and $ [\dfrac{x^2}{2}]_{0}^{\pi} \int_0^{\pi} x \cos x dx=\dfrac{\pi^2}{2}+[x \sin x+\cos x]_{0}^{\pi}$ or, $\dfrac{\pi^2}{2}+\pi \sin \pi-0+\cos \pi-\cos 0=\dfrac{\pi^2}{2}-2$
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.