Higher-order Newton-Cotes formulas are numerical integration techniques that extend the basic idea of approximating the area under a curve by using polynomial interpolation of increasing degrees. These formulas utilize equally spaced sample points and provide more accurate approximations of definite integrals compared to lower-order methods, by considering more data points and increasing the polynomial degree used in the interpolation process. This enhanced accuracy makes higher-order Newton-Cotes formulas particularly useful in various applications where precision is essential.
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