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Path integral may refer to: 1  Line integral, the integral of a function along a curve. 2  Functional integration, the integral of a functional over a space of curves. 3  Path integral formulation of quantum mechanics using functional integration, due to Richard Feynman.
The work per unit charge done by the electric field along an infinitesmal path length ds is given by the scalar product Then the work done against the field per unit charge in moving from A to B is given by the line integral: