The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

formulas for approximating definite integrals by means of the values of the integrand at a finite number of points. The most common quadrature formulas have the form

where x1x2, …, xn are the nodes of the quadrature formula, A1, A2 . . . ,An are its coefficients, and Rn is the remainder term. For example,

where a ≤ ξ ≤ b (trapezoidal rule). Sometimes for mulas for mechanical, or numerical, quadrature are also called quadrature formulas.

### REFERENCE

Krylov, V. I. Priblizhennoe vychislenie integralov, 2nd ed. Moscow, 1967.
The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
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Quadrature formulas based on rational interpolation.
USPENSKY, On the convergence of quadrature formulas related to an infinite interval, Trans.
Stancu, "Quadrature formulas with multiple Gaussian nodes," Journal of the Society for Industrial and Applied Mathematics Series B Numerical Analysis, vol.

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