Theorem 2.3( Composite Simpson Rule). Suppose that [a, b is subdi vided into 2M subintervals [ak, Ck+1] of equal width h=(b-a)/(2M) by using k=a+hh for k=0, 1, .. 2M. The composite Simpson rule for 2M subintervals can be expressed in any of three equivalent ways S(,b)=3>(a22)+4f(x2-)+(a)(2 or S(,2310+4f1+22+4+…+212M-2+4f2M-1+f2)(2.25) 4h M S(,b)=(f(a)+f(b)+3∑f(x2)+3∑f(21).(20 This is an approximation to the integral of f(a)over a, bl, and we write f()d≈S(f,b) (227)