Corollary 2.3(Simpson's Rule: Error Analysis ) Suppose that a, b is subdivided into 2M subintervals [ ak, k+1 of equal width h=(b-a)/(2M The composite Simpson rule S(f,b)=f()+)+∑fa2)+a∑f(a-1)(236) k=1 k=1 is an approximation to the integral A f(aydr=S(f, h)+Es(f, h) (2.37) Furthermore, if f e C a, b], there exists a value c with a c< b so that the error term Es (f, h)has the form b-af(4)(c)h O(h 2.38