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  • $\begingroup$ I don't think it answers my questions at all. I know this, I want to understand it in terms of variation. $\endgroup$ Commented Nov 10, 2023 at 15:31
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    $\begingroup$ You vary the paths that you take. A variation $\delta\int_{a}^{b}\vec{F}\cdot\mathrm{d}\vec{s}$ is typically obtained by varying the curves along which the integral is taken. So you at first parametrize the path from a to b and then you can vary the parametrization under the condition that both starting and finishing point remain the same. The curves $c$ and $\gamma$ can be chosen arbitrarily and thus offer you the opportunity to vary. $\endgroup$ Commented Nov 10, 2023 at 15:40
  • $\begingroup$ Yeah, I agree but it doesn't have that rigor(by the use of variation). $\endgroup$ Commented Nov 10, 2023 at 15:42