Proofs of Stokes Theorem without Differential Forms

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Hello, does anyone have reference to(or care to write out) fully rigorous proof of Stokes theorem which does not reference Differential Forms? I'm reviewing some physics stuff and I want to relearn it.

I honestly will never use the higher dimensional version but I still want to see a full proof in the 3d case - my analysis texts use differential forms and my calculus books don't provide a real proof. I could learn differential forms but I will not use it and I will then forget, making it kind of a waste of time.
 

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