Is it possible to calculate the integral in this way?

Question

First. feel free to change the name of the question, because frankly I didn't know how to name it properly.

Question: I should calculate an integral like this.

Integral(@(r,theta,phi,k) f(r, theta, phi, k)*sin(delta(k)), rmin, rmax..., kmin, kmax)

I have a separate code which calculates the delta(k) separately and returns values of delta in N points. So, as it takes much time I want to calculate and create an array of delta then put it under the integral. But as the k is a variable in integral, what should I do. Can I pass a data set to the function under integration.

After getting the delta array I tried to fit it to get a function to put it in the integral, but this option is not precise enough.