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    %% Integrand with Singularity on Integration Boundary
% Integrate the function
%
% $$\left[ \left( x+y \right)^{1/2} \left(1+x+y\right)^2\right]^{-1}$$
%
% over the region $0 \le x \le 1$ and $0 \le y \le 1-x$. This integrand is
% infinite at the origin (0,0), which lies on the boundary of the
% integration region. 
fun = @(x,y) 1./(sqrt(x + y) .* (1 + x + y).^2 );
ymax = @(x) 1 - x;
Q = quad2d(fun,0,1,0,ymax)

%%
% The true value of the integral is $\pi /4 - 1/2$.
pi/4 - 0.5