Editing Generalized Stokes theorem (section)

===Divergence theorem===
Likewise, the [[divergence theorem]]
<math display="block">\int_\mathrm{Vol} \nabla \cdot \mathbf{F} \, d_\mathrm{Vol} = \oint_{\partial \operatorname{Vol}} \mathbf{F} \cdot d\boldsymbol{\Sigma}</math>
is a special case if we identify a vector field with the <math>(n-1)</math>-form obtained by contracting the vector field with the Euclidean volume form. An application of this is the case <math>\textbf{F}=f\vec{c}</math> where <math>\vec{c}</math> is an arbitrary constant vector. Working out the divergence of the product gives
<math display="block">\vec{c} \cdot \int_\mathrm{Vol} \nabla f \, d_\mathrm{Vol} = \vec{c} \cdot \oint_{\partial \mathrm{Vol}} f\, d\boldsymbol{\Sigma}\,.</math>
Since this holds for all <math>\vec{c}</math> we find
<math display="block">\int_\mathrm{Vol} \nabla f \, d_\mathrm{Vol} = \oint_{\partial \mathrm{Vol}} f\, d\boldsymbol{\Sigma}\,.</math>