I am trying to find the surface area.

So I know that once I have the parameters, I can find Tu, Tv and cross them to find the normal vector.

However, I seem to have trouble whenever the function isn't given in terms of u and v.

This is the problem I am looking at:-

Calculate [Double Integral] f(x,y,z)dS for the given surface and function

y=9-z^2, 0<=x<=3, 0<=z<=3, f(x,y,z) = z