Integration, numerical

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Finding an integral by numerical methods. Numerical integration is applied when the integrand is approximately given (by a table), or, if it is given exactly, when numerical integration leads to a result within given accuracy much faster than the use of exact methods, or, finally, if the use of exact methods is impossible since the integral cannot be expressed in terms of known functions. Quadrature (in the case of one variable) and cubature (for calculating multiple integrals) formulas have been derived for numerical integration (cf. Quadrature formula; Cubature formula).

See also Interpolation in numerical mathematics.


[a1] G. Dahlquist, A. Bjorck, "Numerical methods" , Prentice-Hall (1974) pp. §7.4
[a2] J. Stoer, R. Burlirsch, "Introduction to numerical analysis" , Springer (1980) pp. Chapt. 3 (Translated from German)
[a3] F.B. Hildebrand, "Introduction to numerical analysis" , Dover, reprint (1987) pp. Chapt. 8
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Integration, numerical. Encyclopedia of Mathematics. URL:,_numerical&oldid=53818