The Curl Integral Theorem combines the rotation $$\nabla \times \boldsymbol{F}$$ of a vector field $$\boldsymbol{F}$$ within a surface $$A$$ with the line integral of the vector field along the edge $$L$$ of the considered surface $$A$$: $\int_{A} (\nabla \times \boldsymbol{F}) \cdot \text{d}\boldsymbol{a} ~=~ \oint_{L} \boldsymbol{F} \cdot \text{d}\boldsymbol{l}$