2D integration over an area whose boundary is specified by Fourier series

Dear All,

I have an arbitrary surface whose boundary is determined by a Fourier series in (r,z) coordinate system. This boundary is specified in terms of (s,t) by the following parametric equations:

r = 1+s*cos(t)
z = s*sin(t)
s = f(t) = sum(n=0, infinity) an*cos(n*t) % Fourier series: an is the n'th coefficient.

How can I perform integration of a function G(r,z) over the area which is enclosed by the boundary?

integral( G(r,z)drdz )

Thanks,

Ahmad