Simpson rule
3-points Newton-Cotes formulas.
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\[\begin{eqnarray} \int_{a}^{b} f(x) \ dx & \approx & \frac{ \delta x }{ 3 } \left( f(x_{0}) + 4 f(x_{1}) + 2 f(x_{2}) + 4 f(x_{3}) + 2 f(x_{4}) + \cdots + 4 f(x_{n-1}) + 2 f(x_{n}) \right) . \nonumber \end{eqnarray}\]