Computations of Definite Integrals Using the Residue Theorem

Abstract

We have seen in Chapter 5 how the fundamental theorem of calculus for line integrals, or Cauchy’s theorem, allow us to compute integrals such as the Fresnel integrals. In that section no residues are computed. The approach in the present section is different. The main player is the residue theorem. There are numerous kinds of definite integrals which one can compute using this theorem, and in the present chapter we do not try to be exhaustive.