Engineering Mathematics

Get full access to Engineering Mathematics and 60K+ other titles, with a free 10-day trial of O'Reilly.

There are also live events, courses curated by job role, and more.

14.7 EVALUATION OF REAL DEFINITE INTEGRALS

We shall now discuss the application of Cauchy's Residue theorem to evaluate real definite integrals.

(A) Integration around the unit circle

We consider the integrals of the type

where the integrand is a rational function of sin θ and cos θ. Substitutet z = e^iθ. Then, dz = i e^iθ 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 ...

Get Engineering Mathematics now with the O’Reilly learning platform.

O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.

Start your free trial

Don’t leave empty-handed

Get Mark Richards’s Software Architecture Patterns ebook to better understand how to design components—and how they should interact.

It’s yours, free.

Get it now

Check it out now on O’Reilly

Dive in for free with a 10-day trial of the O’Reilly learning platform—then explore all the other resources our members count on to build skills and solve problems every day.

Start your free trial Become a member now