Cotes Integration Formulas

formulas used for approximating definite integrals using the values of the integrand at a finite number of equally spaced points, that is, quadrature formulas with equally spaced nodes. The Cotes integration formulas have the form

The numbers a_k⁽ⁿ⁾ are called the Cotes coefficients and are determined under the condition that the formula (*) is exact whenever f( x) is a polynomial of degree not greater than n. The Cotes integration formulas were introduced by the British mathematician R. Cotes (1682–1716).