Residue and its Application in Real Integrals

Abstract

     The residue theorem is a powerful tool in calculating real integrals. This theorem allows us to easily solve the integrals by converting them into complex integrals and calculating the residue. The purpose of this research is the residue theorem and its application in real integrals. This research has been collected using the library method. We have achieved these results that integrals have many applications in different fields of science. Of course, this method is usually for more complex integrals and functions that are descending on the real axis useful. In this method, we expand the real integral to a mixed integral, we calculate the residues, which is usually simple. We calculate the integral around this curve using the residue theorem. With this method, complex integrals can be calculated more accurately. Not all integral able functions can be integrated using preliminary methods.