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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 \(A\): \[ \int_{A} (\nabla \times \boldsymbol{F}) \cdot \text{d}\boldsymbol{a} ~=~ \oint_{L} \boldsymbol{F} \cdot \text{d}\boldsymbol{l} \]