Editing Cauchy's integral theorem (section)

{{Short description|Theorem in complex analysis}}
{{Distinguish|Cauchy's integral formula|Cauchy formula for repeated integration}}

{{Complex analysis sidebar}}
In [[mathematics]], the '''Cauchy integral theorem''' (also known as the '''Cauchy–Goursat theorem''') in [[complex analysis]], named after [[Augustin-Louis Cauchy]] (and [[Édouard Goursat]]), is an important statement about [[line integral]]s for [[holomorphic function]]s in the [[complex number|complex plane]]. Essentially, it says that if <math>f(z)</math> is holomorphic in a [[simply connected]] [[Domain (mathematical analysis)|domain]] Ω, then for any simply closed contour <math>C</math> in Ω, that contour integral is zero. 

<math display="block">\int_C f(z)\,dz = 0. </math>