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I am trying to get a useful heuristic picture of a line integral, like the area

under a curve for an ordinary integral. My current one is: if I place a particle

in a force field, then the line integral from point A to B is the change in kinetic energy

of the particle from A to B. This works for simple cases, but not

for something like the circulation of the magnetic field, which does no work.

Are there any more accurate ways to picture a line integral of a vector field?

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# How to visualize a line integral

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