# Time dependent three dimensional dirac delta function

1. Nov 28, 2015

### chiraganand

Ok so for equations of spherical wave in fluid the point source is modeled as a body force term which is given by time dependent 3 dimensional dirac delta function f=f(t)δ(x-y) x and y are vectors.
so we reach an equation with ∫f(t)δ(x-y)dV(x) over the volume V. In the text book it then says that using sampling properties of dirac delta over a small spherical volume
∫f(t)δ(x-y)dV(x)=-f(t)
Can someone please explain to me what this means?? and how the final answer was got?
I know the properties of the dirac delta function but here it's time dependent and 3d so how do i get the corresponding answer?
The book is Fundamentals of Non destructive evaluation by lester schmerr

2. Nov 28, 2015

### MarcusAgrippa

The time dependent factor f(t) is not part of the delta function. It therefore can be taken out of the integration, since the integral does not involve time. This leaves you wth an integral over all space of the delta function, which equals 1.

3. Nov 28, 2015

### chiraganand

Ah alright.. I thought this would be the answer but wasn't sure.. thanks a ton!!