# Improper integrals

1. Mar 16, 2014

### Panphobia

1. The problem statement, all variables and given/known data

$\int_{-\infty}^{+\infty} e^{-\left|x\right|} \,dx$

3. The attempt at a solution
So I know you are supposed to split this integral up into two different ones, from (b to 0) and (0 to a) where b is approaching - infinity, and a is approaching +infinity, but how would I take that antiderivative? Since the absolute value has a piecewise derivative.

2. Mar 17, 2014

### Pranav-Arora

Hi Panphobia!

Do you see you can write it as $\int_{-\infty}^0 e^x\,dx +\int_0^{\infty} e^{-x}\,dx$?

3. Mar 17, 2014

### Panphobia

I totally missed that, but yea I see it now, thanks!

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