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In even simpler terms, one can consider that points can be thought of as the boundaries of curves, that is as 0-dimensional boundaries of 1-dimensional manifolds.
So, just like one can find the value of an Integral ( f = dF ) over a 1-dimensional manifolds () by considering the anti-derivative ( F ) at the 0-dimensional boundaries (), one can generalize the fundamental theorem of calculus, with a few additional caveats, to deal with the value of integrals ( dω ) over n-dimensional manifolds ( Ω ) by considering the anti-derivative ( ω ) at the ( n-1 )- dimensional boundaries ( dΩ ) of the manifold.

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