A double integration of the tabulated data.

A double integration of the tabulated data.

A double integration of the tabulated data. f(x,y) may be generated in terms of meshgrid. Double integral computes simply by approximation of the integral for f(x,y) via the trapezoidal method.
Firstly, an integration loop within inner integral over X is performed obtaining the function of area A(y). Secondly, outer loop integration is performed for A(y) over y limits
Example:
Q = dblquad(inline('y*sin(x)+x*cos(y)'), pi, 2*pi, 0, pi);
Q = -9.8696
[X,Y] = meshgrid(pi:pi/100:2*pi, 0:pi/100:pi );
Z=Y.*sin(X)+X.*cos(Y);
int_2D_tabulated(X,Y, Z )
ans = -9.8688