linguistic:voice_change, information:classification, information:extraction
Fundamental theorem of line integrals

The fundamental theorem of line integrals says that a line integral through a gradient field can be evaluated by evaluating the original scalar field at the endpoints of the curve.

Let φ: U ⊆ R 2 → R {\displaystyle \varphi:U\subseteq \mathbb {R} ^{2}\to \mathbb {R} }. Then

with p, q the endpoints of the curve γ.