In mathematics, a path integral is an integral where the function to be integrated is evaluated along a path or curve. Various different path integrals are in use.
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Complex analysis
The path integral is a fundamental tool in complex analysis, where it is also called a contour integral. Suppose U is an open subset of C, γ : [a, b] → U is a rectifiable curve and f : U → C is a function. Then the path integral
If γ is a continuously differentiable curve, the path integral can be evaluated as an integral of a function of a real variable: