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February 25th, 2018, 08:49 AM  #1 
Senior Member Joined: Jan 2016 From: Blackpool Posts: 103 Thanks: 2  Contour line integral question
By rewriting the integral as a contour integral around the unit circle C(0, 1) show that \[\int_{0}^{2\pi}\frac{1}{2+isin(\theta)}d\theta=2pi/\sqrt{5}\] Last edited by Jaket1; February 25th, 2018 at 08:52 AM. 
April 25th, 2018, 03:49 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
That function is $\displaystyle \frac{1}{2+ isin(z)$ restricted to the unit circle. Since this is a closed contour, the integral is equal to the sum of its residues inside the unit circle. Where does the function have poles?


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