Can the Integral of a Multi-Gaussian be Evaluated for a Function of x and y?

[forumfann]

Could anyone help me evaluate the integral
$\intop_{-\infty}^{\infty}\intop_{-\infty}^{\infty}|sx+ty|e^{-s^{2}/2}e^{-t^{2}/2}dsdt$, which should be a function of x and y?

By the way, this is not a homework problem.

Thanks

 

[mathman]

You will have to divide the domain of integration into two parts along the line sx+ty=0 (for fixed x and y) and integrate separately. I believe the result will involve erf (integral of Gaussian).