− ∫ a b F ⋅ d l = P ( b ) − P ( a ) , -\int _{a}^{b}\mathbf {F} \cdot d\mathbf {l} =P(\mathbf {b} )-P(\mathbf {a} ), where the integration is over a Jordan arc passing from location a to location b and P(b) is P evaluated at location b. ∮ F ⋅ d l = 0 , \oint \mathbf {F} \cdot d\mathbf {l} =0, where the integral is over any simple closed path, otherwise known as a Jordan curve. ∇ × F = 0. {\displaystyle {\nabla }\times {\mathbf {F} }=0.}