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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
 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
 one year ago

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qwerty54321Best ResponseYou've already chosen the best response.0
Could you explain why please?
 one year ago

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

SpacelimbusBest ResponseYou've already chosen the best response.0
can 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.
 one year ago

qwerty54321Best ResponseYou've already chosen the best response.0
sorry here is the problem with proper notations
 one year ago

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

qwerty54321Best ResponseYou've already chosen the best response.0
if it is not a closed curve, would the second part still hold true?
 one year ago

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