# Help with proof for Dirca Delta Relation

1. Oct 2, 2006

### orion141

I cannot think of how to go about proving this relationship and was wondering if any of you could help me

$$</font>\\int^{\\infty}_{-\\infty} f(x) \\delta \\left( g \\left( x \\right) \\right) dx = \\int^{\\infty}_{-\\infty} f(x) \\sum_{i} \\frac{\\delta \\left( x - x_{i} \\right)}{\\left| g' \\left( x_{i} \\right) \\right|} dx,<font color=red>$$

Thanks
Tom

2. Oct 2, 2006

### orion141

I am not too good with this latex stuff so let me try again...

$$\\int^{\\infty}_{-\\infty} f(x) \\delta \\left( g \\left( x \\right) \\right) dx = \\int^{\\infty}_{-\\infty} f(x) \\sum_{i} \\frac{\\delta \\left( x - x_{i} \\right)}{\\left| g' \\left( x_{i} \\right) \\right|} dx$$

3. Oct 2, 2006

4. Oct 2, 2006