# Integral over a sphere with the dirac delta function

1. Aug 7, 2009

### tim85ruhruniv

1. The problem statement, all variables and given/known data

$$$\underset{\left|\underline{\xi}\right|=1}{\int}\delta_{0}\left(\underline{\xi}\cdot\underline{z}\right)dS_{\xi}=\intop_{0}^{2\pi}d\varphi\intop_{-r}^{+r}\delta_{0}\left(\varsigma\right)\frac{d\varsigma}{r}=\frac{2\pi}{r}$$$

The $$\delta_{0}$$ is the dirac delta function.

the following variable substitution has been made,
$$$\varsigma=\underline{\xi}\cdot\underline{z}=rcos\theta$$$

2. Relevant equations

I am not really sure whether its over the surface of the sphere or the Volume,

the problem and the solution are given above, I want to know how it has been solved.
What is the Jacobian Determinant for the problem ?

3. The attempt at a solution

I always end up with $$2\pi$$

Last edited: Aug 7, 2009
2. Aug 7, 2009

### tim85ruhruniv

hey guys,

thanx a lot but i got it finally.

by the way... i posted this problem in another section too and i dont know how to delete it...

Thanx...