June 2009
Intermediate to advanced
1100 pages
42h 22m
English
We shall now discuss the application of Cauchy's Residue theorem to evaluate real definite integrals.
We consider the integrals of the type

where the integrand is a rational function of sin θ and cos θ. Substitutet z = eiθ. Then, dz = i eiθ dθ = iz dθ and

Thus (47) converts inZto the integral
where φ(z) is a rational function of z and C is the unit circle ...