Advanced Engineering Mathematics, 7th Edition

19.6 Evaluation of Real Integrals

INTRODUCTION

In this section we shall see how residue theory can be used to evaluate real integrals of the forms

(1)

(2)

(3)

where F in (1) and f in (2) and (3) are rational functions. For the rational function f(x) = p(x)/q(x) in (2) and (3), we will assume that the polynomials p and q have no common factors.

Integrals of the Form F(cos θ, sin θ) d θ

The basic idea here is to convert an integral of form (1) ...