This paper gives a numerical integration rule for integrating functions over any n-dimensional cube. The rule is derived using a simple linear transformation of the given n-cube to a zero-one cube. The prescribed method is proved to be superior in a certain sense to the existing integration formulae. The performance of the method is illustrated for different type of integrands over different n-dimensional cubes.
Sarada Jayan and Dr. K.V. Nagaraja, “Numerical integration over n-dimensional cubes using generalized gaussian quadrature”, Proceedings of the Jangjeon Mathematical Society, vol. 17, pp. 63-69, 2014.