Evaluate following integrals using simpson's rule and corrected simpson's rule (or richardson extrapolation in case the corrected simpson's is not applicable). In each case, use n = 2,4,8,16,32. Tabulate results, along with error. Use the ratios of successive errors to find p such that error is proportional to n^(-p).
a) integral 0 to 1 of (4/1+x^2) dx
b) integral 0 to 1 of (x^(1/2)) dx