Mr. Integral
Math notes/Calculus III/Vector Calculus

The Divergence Theorem — Cheat sheet

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Core rule

∬∂VF⋅n dS=∭V∇⋅F dV.\iint_{\partial V}\mathbf F\cdot\mathbf n\,dS=\iiint_V\nabla\cdot\mathbf F\,dV.

Watch for

Require a closed outward boundary and a smooth field throughout the enclosed solid.