Questino about integration of differential forms

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Here is the theorem about the integration of two-forms in Edwards' "Advanced Calculus"

The definitions of "charts" in this theorem are given here.

What I do not understand about the Theorem is the orientation of the domain of integration by dudv.

Why do we oriented the domain in this way? Could I orient the domain instead by dvdu?

The "charts" as in the Theorem are not oriented in any particular way; it could be oriented by dudv or dvdu, as long as the orientation of the charts is consisitent.

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1 Answer

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Reversing the orientation (duddv=-dvdu) merely reverses the sign of all integrals. Nobody said you couldn't do it!

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