Stokes’ Theorem — Cheat sheet

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Core rule

∮∂SF⋅dr=∬S(∇×F)⋅n dS.\oint_{\partial S}\mathbf F\cdot d\mathbf r=\iint_S(\nabla\times\mathbf F)\cdot\mathbf n\,dS.

Watch for

Use the right-hand rule. Integrate curl, not the original field, across the surface.