heorem 2.2 (Composite Trapezoidal Rule). Suppose that the inter- val la b is subdivided into M subintervals [ok, k+1 of width h=(b-a)/M by using the equally spaced nodes ck =a+hh, for k=0, 1,..., M. The composite trapezoidal rule for M subintervals can be expressed in any of three equivalent ways r(,b)=∑(f(xk-1)+f(x) k-1 (219) or T(f,h)=x(6+2f1+22+23+…+2fM-2+2fM-1+f or T(, h)=o(f(a)+f(b))+h2 f(ak) (2.21) k=1 This is an approximation to the integral of f(a)over [a, bJ, and we write f()d≈r(f,b (222)