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Integral with e^-|t|

  1. Nov 26, 2008 #1
    I am working through Signals and Systems Demystified on my own. I need to integrate:

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

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

    \int_{-\infty}^{\infty} e^{-|t|} dt = \int_{-\infty}^{0} e^{t} dt + \int_{0}^{\infty} e^{-t} dt

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

  2. jcsd
  3. Nov 26, 2008 #2
    The expansion is correct.
  4. Nov 28, 2008 #3
    Use the decomposition you have now and do integration by parts twice (on each decomposed integral). I think you'll be pleasantly surprised.
  5. Dec 8, 2008 #4
    That worked. Thanks!
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