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
Solutions:
Poles of integrand are given by
Hence by Cauchy’s Residue Theorem