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Question of the Day: Complex Analysis

Cauchy's Residue Theorem is as follows:

Let  be a simple closed contour, described positively. If a function  is analytic inside  except for a finite number of singular points  inside , then 

For the following problem, use a modified version of the theorem which goes as follows:

Residue Theorem

If a function  is analytic everywhere in the finite plane except for a finite number of singular points interior to a positively oriented simple closed contour , then

 

Brown, J. W., & Churchill, R. V. (2009). Complex variables and applications. Boston, MA: McGraw-Hill Higher Education.

Use the Residue Theorem to evaluate the integral of

  

in the region .

0

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