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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

Spring 2009 • Question 10

Question

Math 6210 • Real Analysis Spring 2009 • Question 10

Suppose \(a\) is a real number greater than \(1\). Compute \[ \int _0^{2\pi }\frac {d\theta }{a+\sin \theta } \] using residues. Hint: \(\sin \theta =\frac {z-z^{-1}}{2i}\) where \(z=e^{i\theta }\).

Raw LaTeX

Suppose \(a\) is a real number greater than \(1\). Compute
\[
\int_0^{2\pi}\frac{d\theta}{a+\sin\theta}
\]
using residues. Hint: \(\sin\theta=\frac{z-z^{-1}}{2i}\) where \(z=e^{i\theta}\).

Topic Tags

Isolated Singularities and Residues Lebesgue Integration