I am tying to integrate log(ri)*log(rj)*ds over the boundary of the unit circle, i,j=1,....,N. Where s is a curvilinear co-ord along the boundary of the domain and ri is the eucledian distance between a point in the unit circle (x,y) and a point outside of the domain. I want to implement this on Matlab using Simpson's Rule. The answer should fill an NxN matrix A, with Ai,j=Integral(log(ri)*log(rj))ds So far I have calculated the integrand for a chosen (x,y) and have the values stored in an NxN matrix. I have written working code for Simpson's rule but am not sure how to apply it to this problem. Does my chosen (x,y) have to be on the boundary of the domain since that is what I am integrating over? Any suggestions would be extremely helpful. Thanks in advance.