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``Re: Proof of green's theorem'' by castilladelcarpio on 2008-11-17 09:45:45
For that simple version of Green T you need that the region R be of "type I" and "type II" at the same time.
This means that

If R is of type I it can be described as
{ (x,y) / a < x < b, C(x) < y < D(x) }

If R is of type II it can be described as
{ (x,y) / c < y < d, A(y) < y < B(y) }.

I think that only if the functions involved -that is, A,B,C,D- are monotonic, you can build a region of type III.
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