You have a surface. (Not a curve as I might say.) How do you compute the area under that surface? Simple. Just call trapz twice. Thus once in x, once in y. And trapz can do the job easily enough.
First, I'll make up some data to form a surface, where I know the true answer just so we can see if it works. (Well, I know it works...)
x = linspace(0,pi,20);
y = linspace(0,pi,30)';
z = sin(x).*sin(y);
surf(x,y,z)
Now, I expect the area under the surface to be 4.
syms X Y
int(int(sin(X)*sin(Y),X,[0,pi]),Y,[0,pi])
ans =
4
WHEW! The memory still works. You lose it if you don't use it. ;-)
dx = x(2) - x(1);
dy = y(2) - y(1);
Now, if you use trapz to integrate along one of the dimensions (first I did x), we get a vector. So ONE result for each value of y.
trapz(dx,z,2)
It is exactly as we did before, with nested calls to int. Integrate on x and then y.
trapz(dy,trapz(dx,z,2),1)
Nd that worked quite well. Not exact, but then, this is just trapezoidal rule.
