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Math Help - integral with absolute value

  1. #1
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    integral with absolute value

    I need some help integrating :
     \int e^{-|y|}e^{ty} dy
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  2. #2
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    Quote Originally Posted by lllll View Post
    I need some help integrating :
     \int e^{-|y|}e^{ty} dy
    You just have to split it up as a sum of two integrals, by considering saparately the intervals on which y is positive and negative:

     \int e^{-|y|}e^{ty}\, dy = \int_{y\leqslant0} e^{y}e^{ty}\, dy + \int_{y\geqslant0} e^{-y}e^{ty}\, dy = \int_{y\leqslant0} e^{(t+1)y}\, dy + \int_{y\geqslant0} e^{(t-1)y}\, dy
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