# Quadrature Formulas

The following article is from

*The Great Soviet Encyclopedia*(1979). It might be outdated or ideologically biased.## Quadrature Formulas

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 *x*_{1}*x*_{2}, …, *x*_{n} are the nodes of the quadrature formula, *A _{1}, A_{2} . . . ,A_{n}* are its coefficients, and R

_{n}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.