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Improper integrals

  1. Mar 16, 2014 #1
    1. The problem statement, all variables and given/known data

    [itex]\int_{-\infty}^{+\infty} e^{-\left|x\right|} \,dx[/itex]

    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. jcsd
  3. Mar 17, 2014 #2
    Hi Panphobia!

    Do you see you can write it as ##\int_{-\infty}^0 e^x\,dx +\int_0^{\infty} e^{-x}\,dx##?
  4. Mar 17, 2014 #3
    I totally missed that, but yea I see it now, thanks!
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