Show that F is conservative assuming it's values depend only on endpoints.

1. Nov 19, 2009

phantomcow2

Assuming that the value of $$\int\$$F $$\bullet$$dr, then F is a conservative function.

The class is Calc 3. My professor went through this proof in class but it was the one proof in this section that I didn't fully comprehend. Usually I try to find the proof from another source, such as online, to solidify my understanding. I'm unable to find this proof, though.

Can anybody link me to where this proof is recited, or even if it has a formal name?
Thanks.

2. Nov 19, 2009

phantomcow2

PS. Sorry for the crappy latex formatting. There should be a "C" underneath the integral sign, and that's supposed to be the vector valued function F dotted with dr, the parametrization of curve C. Thank you.

3. Nov 20, 2009

HallsofIvy

Staff Emeritus
The proof depends stongly on the precise definition of "conservative". Some texts use "the integral depends only on the endpoints" as the definition of "conservative" in which case there is nothing to prove! What definition does your textbook use?