Interpolando tres puntos \( (x_{0}, f(x_{0})) \), \( (x_{0}+h, f(x_{0}+h)) \) y \( (x_{0}+2h, f(x_{0}+2h)) \), mediante un polinomio de Lagrange e integrando $$ \begin{equation*} I = \frac{1}{3} h \ [f(x_{0}) + 4 f(x_{0}+h) + f(x_{0}+2h)] \end{equation*} $$
Usando la notación acostumbrada $$ \begin{equation*} I = \frac{1}{3} h \ [f(x_{i}) + 4 f(x_{i+1}) + f(x_{i+2})] \end{equation*} $$