# Evaluate by Contour Integration

I am able to solve this problem by Cauchy Residue theorem, but not by contour integration. (i.e Taking integration in semicircle of radius R and x-axis from -R to +R). $$I = \int_0^{2\pi} \frac{1}{1-2a\cos(t)+a^2}dt\,.$$

$$Given : a^2 < 1$$

PS: Not a homework question, but practice question

• What is the question? – zokomoko Aug 13 '17 at 20:15
• The contour is a circle here. – FDP Aug 13 '17 at 20:24
• Choosing $z$ correctly $\cos(t) = \frac{z+z^{-1}}{2}$ – reuns Aug 13 '17 at 20:36
• @zokomoko Finding the given integral using contour integration. – user1611542 Aug 13 '17 at 20:40
• @FDP I got your point. Thanks! – user1611542 Aug 13 '17 at 20:41