Improper integrals

  • Thread starter Panphobia
  • Start date
  • #1
435
13

Homework Statement



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

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.
 

Answers and Replies

  • #2
3,812
92

Homework Statement



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

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.

Hi Panphobia!

Do you see you can write it as ##\int_{-\infty}^0 e^x\,dx +\int_0^{\infty} e^{-x}\,dx##?
 
  • #3
435
13
I totally missed that, but yea I see it now, thanks!
 

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