Lecture 15 | Integration through a Branch Cut | Example 4 | Theta Classes

In this lecture we are going to solve an improper integral involving multi valued function by the method of contour integration. When multi valued function is present in integrand an additional singularity named Branch point is also there and in order to avoid this we select a special contour called keyhole contour. After that we find poles of integrand and then locate them in the z plane and then we apply Cauchy Residue Theorem. And then after some calculation we get a value of that given integral. If anyone finds any difficulty in understanding this lecture or any step is not clear then do write it in the comment section. Keep connected with Theta Classes to study various topics of higher mathematics. I am providing links of concepts which we used in solving the given improper integral: Multi valued function, Branch point and Branch cut :    • Branch Point and Branch Cut |Multi valued ...   Singularities and its types :    • Types of Singularity in complex analysis|I...   How to find poles :    • example of singularity in complex analysis...   Cauchy Residue Theorem and its proof :    • Cauchy residue theorem|Statement and Proof...   Finding residue at simple pole and pole of order m :    • Residue at a pole|residue at simple pole|r...