Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 7 - Techniques of Integration - Review - True-False Quiz: 13

Answer

False

Work Step by Step

Consider $f(x)=\frac{1}{x}$ and $g(x)=-\frac{1}{x}$, then $\int _{a}^{\infty}f(x)dx$ is divergent and $\int_{a}^{\infty}g(x)$ is divergent, but $\int _{a}^{\infty} (f(x)+g(x)) dx =\int _{a}^{\infty}0 dx=0$ is convergent. Hence, the given statement is false.
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