In
numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods ...
, the Newton–Cotes formulas, also called the Newton–Cotes quadrature rules or simply Newton–Cotes rules, are a group of formulas for
numerical integration
In analysis, numerical integration comprises a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equatio ...
(also called ''quadrature'') based on evaluating the integrand at equally spaced points. They are named after
Isaac Newton
Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, Theology, theologian, and author (described in his time as a "natural philosophy, natural philosopher"), widely ...
and
Roger Cotes.
Newton–Cotes formulas can be useful if the value of the integrand at equally spaced points is given. If it is possible to change the points at which the integrand is evaluated, then other methods such as
Gaussian quadrature
In numerical analysis, a quadrature rule is an approximation of the definite integral of a function, usually stated as a weighted sum of function values at specified points within the domain of integration. (See numerical integration for mor ...
and
Clenshaw–Curtis quadrature are probably more suitable.
Description
It is assumed that the value of a function defined on