How to compute an integral of a complicated function of different variables?

I ‘d like to compute something as follows at certain r and z, but first I must compute the integral and then substituting the r and z values.

A(r, z) = int( f(r,z, teta), teta=0..0.78)

But the problem: f is a complicated function of the 3 variables (including BesselJ(0,..), sin & root square functions, ..!!) thus a simple int command can not compute the integral unless I first substitute the values of the other 2 variables and then integrating; a procedure which seems mathematically wrong (?)

I think there must be another way of integrating (some step by step integrating) (?)

Any help??