NEW APPROACHES TO IRREGULAR INTEGRALS THROUGH THE THEORY OF GENERALIZED FUNCTIONS

In this paper, we investigate a new approach to irregular integrals through the theory of generalized functions. Traditional approaches to irregular integrals are often limited to certain classes of functions or require special techniques to solve singularities. However, through the application of the theory of generalized functions, we open the door to the integration of a wider range of functions that are not strictly defined or have singularities.
In our research, we develop new definitions of irregular integrals based on the principles of the theory of generalized functions. Using this approach, we demonstrate the possibility of integrating functions that were previously beyond the reach of traditional methods. Furthermore, we explore applications of these new definitions in various fields, including mathematics, physics, and engineering.
Our results indicate the potential advantages of this new approach, including greater flexibility when solving problems with singularities, as well as the possibility of application in complex integration problems. Through this work, we open new perspectives in the study of irregular integrals and encourage further research in this area.
Keywords: Irregular integrals, Generalized functions, Singularities, Theory of distributions, Integration of functions with singularities