path independence

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This video provides an example of the work done by a vector field.
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This video explores the effect on the previous line integral of reversing the parametrization of the path of the line.
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This video establishes that the line integral is independent of path direction.
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This video establishes that vector-valued functions, as opposed to scalar functions, are path direction dependent.
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This video establishes the conditions for a line integral of a vector-valued function to be path-independent.
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This video demonstrates that the line integral of a closed curve over a conservative vector field is 0.
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This video provides an example illuminating the previous video.
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This video provides yet another example of a line integral over a closed curve.
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