Cubature

Ueberhuber (1997, p. 71) and Krommer and Ueberhuber (1998, pp. 49 and 155-165) use the word "quadrature" to mean numerical computation of a univariate integral, and "cubature" to mean numerical computation of a multiple integral.

Cubature techniques available in the Wolfram Language include Monte Carlo integration, implemented as NIntegrate[f, ..., Method -> MonteCarlo] or NIntegrate[f, ..., Method -> QuasiMonteCarlo], and the adaptive Genz-Malik algorithm, implemented as NIntegrate[f, ..., Method -> MultiDimensional].

REFERENCES:

Cools, R. "Monomial Cubature Rules Since "Stroud": A Compilation--Part 2." J. Comput. Appl. Math. 112, 21-27, 1999.

Cools, R. "Encyclopaedia of Cubature Formulas." http://www.cs.kuleuven.ac.be/~nines/research/ecf/ecf.html.

Cools, R. "Constructing Cubature Formulae: The Science Behind the Art." In Acta Numerica (Ed. A. Iserles). Cambridge, England: Cambridge University Press, pp. 1-54, 1997.

Cools, R. and Rabinowitz, P. "Monomial Cubature Rules Since "Stroud": A Compilation." J. Comput. Appl. Math. 48, 309-326, 1993.

Krommer, A. R. and Ueberhuber, C. W. "Construction of Cubature Formulas." §6.1 in Computational Integration. Philadelphia, PA: SIAM, pp. 155-165, 1998.

Radon, J. "Zur mechanische Kubatur." Monatsh. Math. 42, 286-300, 1948.

Ueberhuber, C. W. Numerical Computation 2: Methods, Software, and Analysis. Berlin: Springer-Verlag, 1997.