## 17

## Calculus of Residues

#### 17.1 Evaluation of Real Integrals

#### 17.1.1 Introduction

It is interesting to note that the residue theorem provides us with an elegant and simple method for evaluation of certain classes of real integrals, which cannot be evaluated by the usual methods of real calculus. Evaluation of a real definite integral is done by converting it into a contour integral. In order to do this one has to identify

- an appropriate closed contour C and
- a suitable complex function to be chosen as an integrand.

We classify the real integrals to be evaluated under different types, identify the closed contour *C*, the complex function to be integrated in each case and evaluate the integrals. But at first we will briefly study about zeros, singularities ...