Also known as Kelvin-Stokes Theorem, the fundamental theorem for curls, or the curl theorem 3D version of [[Green's Theorem]] The line integaral of a vector field over a loop is equal to the flux of its curl through the loop: $ \oint_C\boldsymbol{F}\cdot d\boldsymbol{r}=\iint_S(\nabla\times\boldsymbol{F})\,d\boldsymbol{S} $