# Numerical integration

method tae obtain approximations o integrals

I the field o numerical analysis, numerical integration (quadrature) is a method tae obtain approximations o integrals[1]. It is usit at the area o numerical methods for ordinary differential equations an numerical methods for pairtial differential equations.

Various formulas have been studiit for many years an become famous. For example, thare is the Gaussian quadrature[2] (namit after Gauss), the Newton-Cotes formula[3] (namit after Isaac Newton), and the Euler-Maclaurin formula[4] (namit after Leonhard Euler).

## References

1. avis, P. J., & Rabinowitz, P. (2007). Methods of numerical integration. Courier Corporation.
2. Weisstein, Eric W. "Gaussian Quadrature." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GaussianQuadrature.html
3. Weisstein, Eric W. "Newton-Cotes Formulas." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Newton-CotesFormulas.html
4. Weisstein, Eric W. "Euler-Maclaurin Integration Formulas." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Euler-MaclaurinIntegrationFormulas.html
5. S.M. Rump: INTLAB - INTerval LABoratory. In Tibor Csendes, editor, Developments in Reliable Computing, pages 77-104. Kluwer Academic Publishers, Dordrecht, 1999.