A new integration method is proposed for integration of arbitrary functions over regions having circular boundaries. The method is developed using a new non-linear transformation which can transform such a region to a zero-one cube. The derivation of this formula over a circular and elliptic cylinder, cone and paraboloid is shown with numerical results.
Sarada Jayan and Dr. K.V. Nagaraja, “Numerical Integration over Three-Dimensional Regions Bounded by One or More Circular Edges”, Procedia Engineering, vol. 127, pp. 347–353, 2015.