section_path: In calculus/Fundamental theorem of line integrals
section_name: Fundamental theorem of line integrals
paragraph_text: 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 n → R {\displaystyle \varphi:U\subseteq \mathbb {R} ^{n}\to \mathbb {R} }. Then