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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