Gaussian integral in two dimensions

[spaghetti3451]

I am trying to evaluate the following integral.

$\displaystyle{\int_{-\infty}^{\infty}f(x,y)\ \exp(-(x^{2}+y^{2})/2\alpha)}\ dx\ dy=1$

How do you do the integral above?

 

[Ssnow]

Hi, it seems evaluated jet $=1$, depends what is $f(x,y)$ and $\alpha$? You must to reformulate the question ...

 

[mathman]

I am trying to evaluate the following integral.

$\displaystyle{\int_{-\infty}^{\infty}f(x,y)\ \exp(-(x^{2}+y^{2})/2\alpha)}\ dx\ dy=1$

How do you do the integral above?

Convert to polar coordinates. Integration is straightforward.