Question

$\underset{0}{\overset{\infty }{\int }}{e}^{-x}dx$

Answer 1

$$\begin{gathered} \mathrm{Let}I={\int }_0^{\infty }{e}^{-x}\mathit{d}x.\mathrm{Then}, \\ I={\left[-e^{-x}\right]}_0^{\infty } \\ \Rightarrow I=-e^{-\infty }+e^0 \\ \Rightarrow I=0+1 \\ \Rightarrow I=1 \end{gathered}$$