## 2D surface integral in MATLAB for Finite Element Calculation

Hi everyone,

As part of a project, I am required to numerically compute the expression

$$b_{i}^{e} &=& \frac{E_{0}^{i}k_0^2(\epsilon_r-1/\mu_r)}{2\Delta^e}\left[\iint\limits_{\Omega^e}(a_i^e + b_i^e x + c_i^e y)e^{-jk_0 x} dx dy\right] \nonumber\\&&- \frac{jk_0 E_0^i r'}{2\Delta^e \mu_r}\left[\int_{\phi_{1}^{s_2}}^{\phi_{2}^{s_2}}(a_i^e \cos\phi + b_i^e r'\cos^2\phi + c_i^e r'\sin\phi\cos\phi)e^{-jk_0r'\cos\phi}d\phi\right]$$

specifically, compute the integrals numerically. The problem is that $\Omega^e$, the domain of integration of the first integral is a triangle (whose vertex coordinates are well known).

I am unable to figure out a way to do this integral computationally in MATLAB. That is, how does one compute an area integral in MATLAB when the x and y coordinates are coupled (and bounded to lie in a spatial region).

If there is a documented way of doing this, or a preexisting function, I would prefer to use it and go ahead with my work, rather than reinvent the wheel. Any inputs would be greatly appreciated!