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 one year ago
Is it true that if F is a plane vector field such that ∮_c(F.dr)=0 for every closed curve C, then ∫_c(F.dr)=0 for every curve C? Please explain.
 one year ago
Is it true that if F is a plane vector field such that ∮_c(F.dr)=0 for every closed curve C, then ∫_c(F.dr)=0 for every curve C? Please explain.

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qwerty54321
 one year ago
Best ResponseYou've already chosen the best response.0Could you explain why please?

klimenkov
 one year ago
Best ResponseYou've already chosen the best response.0Something tells me that it is not right.

Spacelimbus
 one year ago
Best ResponseYou've already chosen the best response.0can you please check your opening post again @qwerty54321, is it all right written out? If F is a potential function then the gradient of that function with dr in a closed path will result to 0, that is true. But I have troubles understanding the post above.

qwerty54321
 one year ago
Best ResponseYou've already chosen the best response.0sorry here is the problem with proper notations

Spacelimbus
 one year ago
Best ResponseYou've already chosen the best response.0I would agree with that yes, for every closed curve C. Path Independance.

qwerty54321
 one year ago
Best ResponseYou've already chosen the best response.0if it is not a closed curve, would the second part still hold true?

Spacelimbus
 one year ago
Best ResponseYou've already chosen the best response.0No in this case it's path independent, but it's integral depends on the value of the end points.
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