- #1
Bipolarity
- 776
- 2
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]
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
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