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Complex oriented curve integral
Formulation 0
Let $\gamma = [w : [a, b] \to \mathbb{C}]$ be an D5650: Continously differentiable oriented complex curve such that
(i) $f : \gamma \to \mathbb{C}$ is a D5635: Standard-continuous complex function on $\gamma$
The complex oriented curve integral of $f$ along $\gamma$ is the D1207: Complex number \begin{equation} \int_{\gamma} f(z) \, d z : = \int^b_a f(w(t)) w'(t) \, d t \end{equation}