step size. This gives

The error of this method is

where is some number between and . Thus, the 3/8 rule is about twice as accurate as the standard method, but it uses one more function value. A composite 3/8 rule also exists, similarly as above.

A further generalization of this concept for interpolation with arbitrary-degree polynomials are the Newton-Cotes formulas.

Composite Simpson's 3/8 rule

Dividing the interval into subintervals of length and

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