Evaluation Of Real Integrals By Contour Integration

Evaluation of Real Integrals by Contour Integration:

For such questions consider a unit radius circle with center at origin, as contour

Now use following relations


We get, the whole function is converted into a function of f (z), Now integral become


where C is unit circle. The value of this integral may be obtained by using Residue Theorem, which is 2πi.(Sum of Residue inside C)

Form I:

Examples: Use residue calculus to evaluate the following integral



Poles of integrand are given by

Hence by Cauchy’s Residue Theorem