1. ## improper integral

evaluate the improper integral :

$\displaystyle \int_0^\infty{e(e^{-x}) \,dx}$

2. Originally Posted by fastman390
evaluate the improper integral :

$\displaystyle \int_{0}^{\infty}e(e^{-x})dx$
If this is what you mean

$\displaystyle \int_{0}^{\infty} e(e^{-x})dx$

Then

$\displaystyle \lim_{b \to \infty} \int_{0}^{b} e(e^{-x})dx=\lim_{b \to \infty} e (-e^{-x})\bigg|_{0}^{b}=$

$\displaystyle \lim_{b \to \infty} -e\cdot e^{-b}+e\cdot e^{0} =e$