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    Hey just trying to integrate |y-x|exp(-0.5(x^2+y^2)) with respect to x, over infinity to minus infinity. I need to have my answer in terms of the error function, tried using a few substitutions and getting kinda close but not really.

    my main issue is finding a substitution that transforms the limits in to those of the form in the error function.

    If anyone could give me tips on where to start that'd be cool.
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    (Original post by Kim-Jong-Illest)
    Hey just trying to integrate |y-x|exp(-0.5(x^2+y^2)) with respect to x, over infinity to minus infinity. I need to have my answer in terms of the error function, tried using a few substitutions and getting kinda close but not really.
    You want to find \displaystyle f(y) =  \int_{-\infty}^\infty |y-x| e^{-\frac{x^2+y^2}{2}} \ dx?
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    (Original post by atsruser)
    You want to find \displaystyle f(y) =  \int_{-\infty}^\infty |y-x| e^{-\frac{x^2+y^2}{2}} \ dx?
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    Well, integrating |x-y| is going to be horrible, but for a fixed y, you can rewrite this as

    \int_{-\infty}^y (y-x)e^{-(x^2+y^2)/2}\, dx + \int_y^\infty (x-y) e^{-(x^2+y^2/2}\, dx

    Then, note that you can easily integrate x e^{-(x^2+y^2)/2}\, dx, you'll be left with a couple of integrals that fairly directly translate into error functions.
 
 
 
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