Home | 18.022 | Chapter 11 | Section 11.5

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When performing this reduction always remember to compute the integral on the easy path; you can only apply Stokes' Theorem to circulation integrals around paths that bound surfaces: all such paths are closed!
The same general approach can be used with the divergence theorem to replace a flux integral over a non-closed surface by the integral of a divergence less a surface integral over additional surfaces which, together with the original surface make a closed one.