Stokes' theorem
Special case of a more general theorem

Stokes' theorem can be viewed as a special case of the following identity: ∮ ∂ Σ (F ⋅ d Γ) g = ∬ Σ g, {\displaystyle \oint _{\partial \Sigma }(\mathbf {F} \,\cdot \,\mathrm {d} {\mathbf {\Gamma } })\,\mathbf {g} =\iint _{\Sigma }\left\mathbf {g},} where g {\displaystyle \mathbf {g} } is any smooth vector or scalar field in R 3 {\displaystyle \mathbb {R} ^{3}}. When g {\displaystyle \mathbf {g} } is a uniform scalar field, the standard Stokes' theorem is recovered.
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