Answer
The integral diverges.
Work Step by Step
We have
$$
\int_{4}^{\infty} \frac{d x}{x^{2/3}}= \int_{4}^{\infty}x^{-2/3}dx\\
=\frac{1}{1/3}x^{1/3}|_4^{\infty}=3(\infty-4^{1/3})=\infty
$$
Hence, the integral diverges.
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 - Chapter Review Exercises - Page 461: 76
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