current loop density delta function representation

[yefj]

Hello i have a current loop with radius "a" (not a small loop).
i have an expression of current density.
I want to verify the expression for J using an integral to get the Current "I",so if i integrate J all over i will get I.
Integral of a function multiplied by delta has a property

How should i construct the integralpropely to get back I?
using cylindrical coordinates.
z from -int to +inf
pho is from zero to +inf
theta is from zero to 2pi
so if i plug them in you can se in the integral bellow that if we use cylindrical system the integral over J doesnt return "I"
Where did i go wrong constructing the cylindrical integral?
Thanks.

 

[wwfeldman]

current density, J, is current/area
to get the current, I, integrate J over the area.

i have no idea what you need a delta function for

the drawing looks more appropriate to finding B due to current in a loop,
not for finding current due to current density