A GENERALIZED APPROACH TO INTEGRATION PROCESS BY AUXILIARY FUNCTIONS

Analytical integrals of functions in closed form are rare and one has to resort frequently to numerical integration techniques. In this work, approximate auxiliary functions that can be integrated are replaced by the original function to determine approximate analytical and numerical integrals. Information on one and two points of the function is used in determining the parameters of the auxiliary trial functions. Three alternative methods are proposed. Once the function without an available closed-form integral is replaced with an integrable one, analytical and numerical integration results can be found. The integration step size can be substantially increased by the employment of the methods.