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1) If we have [itex]\int F \cdot dr[/itex] that is independent of the path, does that mean that the integral will always be 0?

2) For 2 dimensional problems when we evaluate line integrals directly and use Greens Theorem for every piece wise smooth closed curves C, arent we always calculating the area of the curve regardless what the functions f(x,y) and g(x,y) are in

[itex]\int_C F \cdot dr = \int_C f(x,y) dx + g(x,y) dy[/itex]

3) What is the definition of a 'smooth' curve?

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# Confusion over line integrals, Green's Theoreom, Conservative fields

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