I was wondering if there were definitions of arc length similar to the way Darboux integrals define area under a curve (approaching it from upper/lower sums that converge to each). It seems that arc length is defined only using the limit of polygonal under-estimates, but for some reason this doesn't satisfy me, I would like to see that we can construct an over-estimate as well. I have read the other questions on this site pertaining to this topic, and one person mentioned something about convexity and creating an upper bound. Is there any way I could learn how to do this (I'm in Calc 2 right now), I would really like to dig into the theory of why arc length is defined the way it is and if we can define it using upper/lower sums that converge, equivalent to the typical definition. Thanks.
2026-03-28 03:32:02.1774668722
Alternate Arc Length Definitions?
80 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in REAL-ANALYSIS
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