Arclength

Revision as of 00:52, 27 July 2019 by Mag1c (talk | contribs) (how to find arclength of a curve)
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To find the arclength of a curve $y=f(x)$, chop it up into pieces of length $ds$ then add them up to get $\int ds$, as follows:

CartesianArclength



To find the arclength of a curve $r=f(\theta)$, chop it up into pieces of length $ds$ then add them up to get $\int ds$, as follows:

CartesianArclength



It is clear from the diagrams that the polar coordinate version is harder than the cartesian coordinate version, so instead work in terms of $x,y$ and convert to $r,\theta$ as needed.

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