Interpolando cinco puntos \( (x_{0}, f(x_{0})) \), \( (x_{0}+h, f(x_{0}+h)) \), \( (x_{0}+2h, f(x_{0}+2h)) \), \( (x_{0}+3h, f(x_{0}+3h)) \) y \( (x_{0}+4h, f(x_{0}+4h)) \), mediante un polinomio de Lagrange e integrando $$ \begin{equation*} I = \frac{2}{45} h \ [7 f(x_{0}) + 32 f(x_{0}+h) + 12 f(x_{0}+2h) + 32 f(x_{0}+3h) + 7 f(x_{0}+4h)] \end{equation*} $$
Usando la notación acostumbrada $$ \begin{equation*} I = \frac{2}{45} h \ [7 f(x_{i}) + 32 f(x_{i+1}) + 12 f(x_{i+2}) + 32 f(x_{i+3}) + 7 f(x_{i+4})] \end{equation*} $$