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: 19


$$\frac{1}{3 e^{12}}$$

Work Step by Step

\begin{aligned} \int_{4}^{\infty} e^{-3 x} d x &=\lim _{R \rightarrow \infty} \int_{4}^{R} e^{-3 x} d x \\ &=\lim _{R \rightarrow \infty}\left.\frac{e^{-3 x}}{-3}\right|_{4} ^{R} \\ &=\lim _{R \rightarrow \infty} \left(\frac{1}{3 e^{12}}-\frac{1}{3 e^{3 R}} \right) \\ &=\frac{1}{3 e^{12}} \end{aligned} Converges.
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