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qwerty54321
 2 years 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.
qwerty54321
 2 years 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.

This Question is Closed

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

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

Spacelimbus
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.0sorry here is the problem with proper notations

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

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

Spacelimbus
 2 years 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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