The(n+1)-point Newton-Cotes formula for numerical integration is reformulated by expanding its remainder term into series,in particular,the expansions for trapezoidal rule,Simpson's rule and their composite forms are obtained,and it is pointed out that the Romberg integration of higher order can also be worked out by applying the Richardson's extrapolation to the presented expansion based on the composite Simpson's rule instead of Euler-Maclaurin expansion.
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