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: 4



Work Step by Step

$$\lim\limits_{R \to 3-}\int_0^R\frac{dx}{(3-x)^{3/2}}\\= \lim\limits_{R \to 3-}\frac{-1}{-1/2}\frac{1}{(3-x)^{1/2}}|_0^R=2\lim\limits_{R \to 3-}(\frac{1}{\sqrt{3-R}}-\frac{1}{\sqrt 3})\\=3(\infty-1)=\infty.$$ Hence, $\int_0^3\frac{dx}{(3-x)^{3/2}}$ diverges.
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