Double integral using matlab multiplication

Hello, I want to calculate the double integral of an expression (not given here) using matrix multiplication. Using integral2 doesnot work for my case because of singularity issues I will have in that problem. So, first I'm trying out some basic double integral using matrix multiplication but those are not giving me the accurate answer I get calculating analytically.

Integration of sin(th).cos(phi) d(th)d(phi) in the limit of th=0 to pi and phi=0 to 2pi

th=0:pi/180:pi; %theta

phi=0:pi/180:2*pi; %phi

dth2=th(6)-th(5); dphi=phi(6)-phi(5);

int= (dphi.*ones(1,length(phi)))* (cos(phi)'*sin(th))*(dth.*ones(1,length(th)))'; %integration by matrix multiplication

I get answer of 0.0349 instead of 0. Increasing step size to a very massive number helps but that's unreasonable.

Can anyone help, where I'm doing wrong

Answer 1

[Torsten]

th=pi/(2*180):pi/180:pi-pi/(2*180);  %theta
phi=pi/(2*180):pi/180:2*pi-pi/(2*180); %phi
dth=th(6)-th(5); dphi=phi(6)-phi(5);
intvalue= (dphi.*ones(1,length(phi)))*  (cos(phi)'*sin(th))*(dth.*ones(1,length(th)))'

[Saqeeb Adnan]

Thank you so much. So, the singularity at pi/2 was the reason.

[Torsten]

No. In order to approximate a two-dimensional integral, you always have to take the value of the function at the center of a cell, not at the boundary, and multiply it with the area of that cell.