Vanishing of a cyclic integral the property of a state function?

[asdf1]

Why is the vanishing of a cyclic integral the property of a state function?

 

[matt grime]

as far as i can tell, a state function is required to be something whose integral is independent of the path chosen for the integral, this is from searchign with google, and appears to be a thermodynaics thing. if we assume this is the definition of a state function then it is clear why any integral over a loop is zero since we may split the loop into two parts and consider the loop as a path from A to B followed by a path from B to A and the integral over a path from B to A is minus the integral we get if we went along that path backwards so they must add up to zero.

if you're asking why state functions are path independent then could i have your definition of state function.

 

[asdf1]

Thank you~ I understand now.