Originally Posted by

**brandnewdan** Hello

I need to integrate a 2D gaussian function with the gaussian offset by a length b (this creates an annular ring gaussian function with a zero magnitude central region) the function is:

$\displaystyle I=I_0\exp{\frac{-2(r-b)^2}{w^2}}$

and I want to integrate wrt. r and wrt. theta (since this is a rotationally symetric function around r=0), from 0 to infinity and from 0 to 2 Pi

I also need to know how the total area under the following function equates to the answer underneath. Whenever i've tried to integrate this its always come up with some error function which doesn't help me since I need to know a real value for P(infty) given the other variables.

$\displaystyle I=I_0*\exp{\frac{-2r^2}{w^2}}$

$\displaystyle P(\infty)=\frac{I_0w^2\pi}{2}$

Many many thanks in advance

Dan

PS please let me know if I've been unclear. Basically i need to know the area under each function (in closed form so that I can get a value) given that the functions are to be rotated 360 around r=0 to sweep out a 2d shape.