A general and effective numerical integration formula to evaluate all triple integrals with finite limits is proposed in this paper. The formula is derived by transforming the domain of integration to a zero-one cube. The general derivation along with results over specific regions like cuboid, tetrahedron, prism, pyramid and few regions having planar and non-planar faces is provided. Numerical results also are tabulated to validate the formula.
Sarada Jayan and Dr. K.V. Nagaraja, “A General and Effective Numerical Integration Method to Evaluate Triple Integrals Using Generalized Gaussian Quadrature”, Procedia Engineering, vol. 127, pp. 1041–1047, 2015.