12. Theorem 2.1.2 - Cauchy's theorem for C1 images of rectangles.

Let $U \subseteq C$ open, and $f : U \to C$ holomorphic. Let $ϕ : R \to U$ be a $C^{1}$ image of a rectangle. Then given any parametrization of $ϕ (δ R)$ , say $γ$ , we have:
:?:

\int_{γ} f (z) d z := \int_{t_{0}}^{t_{1}} f (γ (t)) γ^{'} (t) d t = 0