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February 25th, 2018, 08:49 AM   #1
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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.
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April 25th, 2018, 03:49 AM   #2
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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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