Corollary 2.3(Simpson,s Rule: Error Analysis). Suppose that a, b is subdivided into 2M subintervals [ ok, k+1 of equal width h=(b-a)/(2M) The composite Simpson rule S(b)=(fa)+f6)+3∑f(2)+∑f(a2-1)(236 is an approximation to the integral f( d r= s(, h)+Es(f, h) (2.37) Furthermore, if f E C4(a, 61, there exists a value c with a <c<b so that the) error term Es(f, h)ha as the form Es(,h)= a)r(4 ()h O(h (2.38) 180