Chapter 8 - Techniques of Integration - 8.7 Improper Integrals - Exercises - Page 440: 16

$$\frac{1}{2 e^{4}}$$

\begin{aligned} \int_{2}^{\infty} e^{-2 x} d x &=\lim _{R \rightarrow \infty} \int_{2}^{R} e^{-2 x} d x \\ &=\lim _{R \rightarrow \infty} \left.\frac{e^{-2 x}}{-2}\right|_{2} ^{R} \\ &= \lim _{R \rightarrow \infty}\left(\frac{1}{2 e^{4}}-\frac{1}{2 e^{2 R}} \right) \\ &= \frac{1}{2 e^{4}} \end{aligned}