ABSTRACT
Reversing the direction of integration, it changes the sign of the integral. The Cauchy’s integral formula is one of the most important consequences of Cauchy’s integral theorem. Most of the definitions and theorems related to an infinite series of real terms can be applied with little changes (or no changes) to series with complex terms. The integration with the residue method is useful in evaluating both real and complex integrals. This method is based on the residue theorem. The residue theorem gives a useful method for evaluating some classes of complicated real definite integrals. The contour must be closed for applying the residue theorem, whereas many integrals of practical interest involve integration over open curves. The ability to evaluate such integrals strongly depends on how the contour is closed, since it requires knowledge of the additional contributions from the added parts of the closed contour.
