Answer
See the proof below.
Work Step by Step
$$\int_1^\infty x^{-2/3}dx=\lim\limits_{R \to \infty}\int_1^Rx^{-2/3}dx\\= \lim\limits_{R \to \infty}\frac{1}{1/3}x^{1/3}|_1^R=3\lim\limits_{R \to \infty}(R^{1/3}-1)\\=3(\infty-1)=\infty.$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 8 - Techniques of Integration - 8.7 Improper Integrals - Exercises - Page 440: 3
Update this answer!
You can help us out by revising, improving and updating this answer.
Update this answerAfter 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.
