In the anisotropic source flux iteration technique for solving the radiation transport problems for evaluating the flux integral, the source within the mesh was approximated to a linear form using the nodal source values. It is shown in this Note that at the start of each iteration, in addition to the nodal sources, the source integral over the mesh is also available. Using the source integral as an additional parameter, several linear approximations and a quadratic approximation for the source distribution within the mesh are possible. This Note discusses the relative merits of the various approximations. A comparative analysis of these approximations with the different difference schemes currently in use is also given. Among the linear schemes, the ones retaining the source integral and the gradient or source integral and the terminal nodal source provide very good accuracy. It is also shown that the quadratic scheme retaining both the nodal sources and the source integral provide far more accurate results without significant increase in computer time or memory.