Poss. for line integral to eval. to 0 w/ non-conservative vector field?

[mathpro18]

Is it possible for a vector field to be non conservative and yet the line integral to evaluate to 0?

 

[Deleted member 4993]

Is it possible for a vector field to be non conservative and yet the line integral to evaluate to 0?

What are the properties of a conservative vector field? Which of those properties are used to prove that theorem about line integral?

What are your thoughts?

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[mathpro18]

What are the properties of a conservative vector field? Which of those properties are used to prove that theorem about line integral?

What are your thoughts?

That the line integral = f(r(a))-f(r(b)) and it only equals 0 if the path is piecewise smooth and closed.

Is it right then to assume of a line integral evaluates to 0 but the vector field is non-conservative that the path is either not piecewise smooth or closed?