Calculations based on the integration of the point kernel over a finite source region are widely used in obtaining gamma-ray fluxes, dose rates, and heating rates. For most cases of practical interest, this integration must be done numerically. The relative merits of the trapezoidal rule, Gauss quadrature, and the semi-Gauss automatic quadrature algorithm of Patterson are discussed as they apply to the integration of the point kernel. The Patterson algorithm is superior to other quadrature algorithms for this application because it allows results to be calculated to a predetermined relative error, wastes no function evaluations, is accurate, and supplies relative error data along with the answer. It is efficient with respect to both engineering and computer time. The implementation of this algorithm for point-kernel integrations is described in detail.