Calculus (3rd Edition)

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


See the proof below.

Work Step by Step

$$\int_1^\infty x^{-2/3}dx=\lim\limits_{R \to \infty}\int_1^Rx^{-2/3}dx\\= \lim\limits_{R \to \infty}\frac{1}{1/3}x^{1/3}|_1^R=3\lim\limits_{R \to \infty}(R^{1/3}-1)\\=3(\infty-1)=\infty.$$
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