## Calculus 8th Edition

Fundamental Theorem of line integrals states that if $C$ defines a smooth curve represented by $r(t)$; $m\leq t \leq n$ and $f$ be a differentiable function with gradient vector $\nabla f$ which is continuous at all points on $C$. Then$\int_C \nabla f.dr=f(r(n))-f(r(m))$