If we divide the polar curve into infinitely thin sectors, the arc length of a single sector can be approximated by [itex] ds = \frac{dθ}{2π}2πr = rdθ[/itex]. So why can't we model the arc length of the curve as [itex] \int^{β}_{α} rdθ[/itex](adsbygoogle = window.adsbygoogle || []).push({});

It turns out that the correct formula is actually

[itex]\int^{β}_{α}\sqrt{r^{2}+(\frac{dr}{dθ})^{2}} \ dθ [/itex]

I know how the correct formula is derived, I just can't figure out why the reasoning for the first formula is incorrect.

BiP

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# Arc length of a polar curve

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