I was interested in finding a motivation for the generalized Stokes' theorem. I was asking myself why(adsbygoogle = window.adsbygoogle || []).push({});

$$ \int_D d \omega = \int_{\partial D} \omega $$ for a region ##D## and a (p-1)-dimensional form ##\omega##.

Then I found something funny when working with some arbitrary functions in two dimensions. Below is what I found.

In the second image, I called ##x^{\mu}_{i}## and ##x^{\mu}_{f}## the coordinates of the initial and final points, respectively.

My question is: Is this actually correct?

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# I Is my understanding correct?

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