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
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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