Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 8 - Techniques of Integration - Chapter Review Exercises - Page 461: 84


The integral converges and its value is $\frac{3}{2}3^{2/3}$.

Work Step by Step

We have $$ \int_{2}^{5} (5-x)^{-1/3} dx=-\int_{2}^{5} (5-x)^{-1/3} d((5-x)\\ =-\frac{1}{2/3}(5-x)^{2/3}|_{2}^{5}=-\frac{3}{2}(0-3^{2/3})=\frac{3}{2}3^{2/3} $$ Hence, the integral converges and its value is $\frac{3}{2}3^{2/3}$.
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.