Integral with e^-|t|

  • Thread starter sam.green
  • Start date
  • #1
6
0
I am working through Signals and Systems Demystified on my own. I need to integrate:

[tex]
\int_{-\infty}^{\infty}{sin(2t)e^{-|t|}e^{-j2\pi ft}} dt
[/tex]

I first went about dealing with the absolute value sign by using the following

[tex]
\int_{-\infty}^{\infty} e^{-|t|} dt = \int_{-\infty}^{0} e^{t} dt + \int_{0}^{\infty} e^{-t} dt
[/tex]

Going along this route seems to not work and makes me think the expansion is incorrect. Can anyone give me a pointer?

Thanks,
Sam
 

Answers and Replies

  • #2
6
0
The expansion is correct.
 
  • #3
256
0
Use the decomposition you have now and do integration by parts twice (on each decomposed integral). I think you'll be pleasantly surprised.
 
  • #4
6
0
That worked. Thanks!
 

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