Perfect Derivative: Line Integral & Why Equal to Zero

[funcosed]

Homework Statement

Could someone explain what a perfect derivative is and why the line integral around a closed loop of a perfect derivative is equal to zero.

Homework Equations

The Attempt at a Solution

 

[Sethric]

I have never heard of the term perfect derivative before, but, from your problem, it sounds like you a referring to an example of a line integral in a field in which the function you are integrating happens to be the derivative of another function:$$\oint f dx$$where either:$$f = \frac {dF} {dx}$$ or: $$f = \nabla \cdot \textbf{F}$$In either case, think about what the fundamental theorem of calculus would imply for a line integral of such a function on a closed loop. If this wasn't what you meant, my mistake, let me know.

 

[funcosed]

Its the case of grad(F) so I guess it means after integrating on the closed loop, when evaluating the limits a and b, we have a = b so its just zero.

I can't find a definition of the term perfect differential, but it was used in my text, which is http://books.google.com/books?id=fh...resnum=4&ved=0CCgQ6AEwAw#v=onepage&q&f=false", in the derivation of circulation theorem on p.88

thanks