How to integrate over a discrete 2D surface in MATLAB?

Question

I have a function z = f(x, y), where z is the value at point (x, y). How may I integrate z over the x-y plan

Answer 1

If you have a discrete dataset for which you have all the x and y values over which z is defined, then just obtain the Zdata matrix corresponding to those (x,y) pairs. Save this matrix, and then you can make it a continuous function using interp2:

function z_interp = fun(x,y)

    z_interp = interp2(Xdata,Ydata,Zdata,x,y);

end

Then you can use integral2 to find the integral:

q = integral2(@fun,xmin,xmax,ymin,ymax)

where @fun is your function handle that takes in two inputs.