Hi Djamel.
One approach is to use the usual Simpson's rule for all but three (consecutive) intervals and use Simpson's 3/8 rule for what is left over. Assume n points 1:n with n even, so there are an odd number of intervals. You can use the usual Simpson's rule on points 1 to n-3 (even number of intervals) and the 3/8 rule at the end. For equally spaced intervals of width h,
Integral = (3*h/8)*(f(n-3) + 3*f(n-2) + 3*f(n-1) + f(n))
Or you could put the 3/8 rule section at the beginning, or somewhere in the middle.
