Contour integration

In the mathematical field of complex analysis, contour integration is a method of evaluating certain integrals along paths in the complex plane.

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${\displaystyle f(a)-f(b)=\int _{b}^{a}f'(t)\,dt}$
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Contour integration is closely related to the calculus of residues, 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.

Contour integration methods include:

• direct integration of a complex-valued function along a curve in the complex plane;
• 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.