Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

2005 • Question 8

Question

Math 6210 • Real Analysis 2005 • Question 8

Evaluate the integral \[ \int _0^{2\pi }\frac {\cos ^2 3\phi }{1-2a\cos \phi +a^2}\,d\phi \] where \(a\) is a complex number such that \(|a|<1\).

Raw LaTeX

Evaluate the integral
\[
\int_0^{2\pi}\frac{\cos^2 3\phi}{1-2a\cos\phi+a^2}\,d\phi
\]
where \(a\) is a complex number such that \(|a|<1\).

Topic Tags

Cauchy Integral Theory and Morera's Theorem Lebesgue Integration