# Contour integration

In the mathematical field of complex analysis, **contour integration** is a method of evaluating certain integrals along paths in the complex plane.[1][2][3]

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Calculus |
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Contour integration is closely related to the calculus of residues,[4] a method of complex analysis.

One use for contour integrals is the evaluation of integrals along the real line that are not readily found by using only real variable methods.[5]

Contour integration methods include:

- direct integration of a complex-valued function along a curve in the complex plane (a
*contour*); - application of the Cauchy integral formula; and
- application of the residue theorem.

One method can be used, or a combination of these methods, or various limiting processes, for the purpose of finding these integrals or sums.