Can anyone help me figure out how to find the constant and integrate this distribution function? $$f(v_x,v_y,v_z) = A \delta(v_z-V_0) e^{-m(v_x^2+v_y^2)/2kT}$$ The integration is because I need to find the flux. I'm not familiar with the delta function.
If I did my work correctly, I would get $$n = \int_{-\infty}^{+\infty} f d^3 v = C \cdot2 V_0 \pi kT /m$$ But again I'm not sure about the delta function and the flux has to be $$ = \int_{-\infty}^\infty f \vec{v} d^3v $$ but I have to find it separately in $x$, $y$ and $z$ directions.