Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 9 - Multiveriable Calculus - Chapter Review - Review Exercises - Page 519: 83



Work Step by Step

We are given $\int^{2}_{0}\int^{1}_{1/2}\frac{1}{y^{2}+1}dydx=\int^{2}_{0}(\int^{1}_{1/2}\frac{1}{y^{2}+1}dy)dx$ solve the inner integral $\int^{1}_{1/2}\frac{1}{y^{2}+1}dy$ $=\frac{1}{y^{2}+1}\int^{1}_{1/2}dy$ $=\frac{1}{y^{2}+1}[x]^{1}_{1/2}$ $=\frac{1}{2y^{2}+2}$ then $\int^{2}_{0}\int^{1}_{1/2}\frac{1}{y^{2}+1}dydx=\int^{2}_{0}\frac{1}{2y^{2}+2}dx$ intergrating $[\frac{1}{2}\ln|2y^{2}+2|]^{2}_{0}$ $=\frac{1}{2}(\ln10-\ln2)$ $=\frac{1}{2}\ln5$
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.