Exercise 1.29. Simpson’s Rule is a more accurate method of numerical integration than the method illustrated above. Using Simpson’s Rule, the integral of a function f between a and b is approximated as
where h = (b – a)/n, for some even integer n, and yk = f(a + kh). (Increasing n increases the accuracy of the approximation.) Define a procedure that takes as arguments f, a, b, and n and returns the value of the integral, computed using Simpson’s Rule. Use your procedure to integrate cube between 0 and 1 (with n = 100 and n = 1000), and compare the results to those of the integral procedure shown above.