Evaluation Of Improper Integrals By Method Of Residue Theorem:- Ukonu, Ejinma O.

Abstract

This work applies the residues theorem which is a concept of the complex calculus to the real calculus. This is significant as the theorem is used for the evaluation of some real definite integrals. First, the residues of a complex function is established from which the residues theorem is stated and proved. These were done with the aid of the Laurent’s series of a complex function and cauchy s integral theorems and formulas. Finally, the theorem is applied to the evaluation of some real definite integrals by appropriate conversions of the real functions to complex ones and selecting suitable contours for their integration.