1. The problem statement, all variables and given/known data The proof begins: Suppose that F is conservative. Then a scalar field ε(r) can be defined as the line integral of F from the origin to the point r. So ∫F dot dr = ε(r), where the limits of integration are from 0 to r. The next step, however, eludes me: From the definition of an integral, it then follows that an infinitesimal change in ε is given by dε = F dot dr. 2. Relevant equations 3. The attempt at a solution Usually total differentials are related to partial derivatives, tangent planes, and Taylor expansions. I'm failing to fill in the intermediate steps in deriving dε = F dot dr from ∫F dot dr = ε(r) using the "definition of integral". Any insight?