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: 21



Work Step by Step

\begin{aligned} \int_{-\infty}^{0} e^{3 x} d x &=\lim _{R \rightarrow-\infty} \int_{R}^{0} e^{3 x} d x \\ &=\lim _{R \rightarrow-\infty} \left.\frac{e^{3 x}}{3}\right|_{R} ^{0} \\ &=\lim _{R \rightarrow-\infty} \frac{1}{3}-\frac{e^{3 R}}{3}\\ &=\frac{1}{3} \end{aligned} Converges.
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