Probability and complex function: Unit IV: Complex integration

Application of residue theorem for evaluation of real integrals as use of circular and semi-circular contour

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The complex integration along the scro curve used in evaluating the definite integral is called contour integration.

APPLICATION OF RESIDUE THEOREM FOR EVALUATION OF REAL INTEGRALS AS USE OF CIRCULAR AND SEMI-CIRCULAR CONTOUR

 

(a) Contour Integration :

The complex integration along the scro curve used in evaluating the definite integral is called contour integration.

Type 1: Integrals of the form  where f is a rational function in cos θ and sin θ.

Suppose the given integral is 

Here, we shall choose the contour as the unit circle


When these results are used in the complex integral, we get



Probability and complex function: Unit IV: Complex integration : Tag: : - Application of residue theorem for evaluation of real integrals as use of circular and semi-circular contour

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