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.