# Arclength

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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:

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:

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.