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ArcLength

Compute the arc length of a curve.

$ wo 'ArcLength[Disk[]]'
Undefined

A parameterized curve ArcLength[curve, {t, a, b}] integrates the speed Sqrt[Sum of squared derivatives] over the range.

$ wo 'ArcLength[{Sin[t], Cos[t]}, {t, 0, 2 Pi}]'
2*Pi

$ wo 'ArcLength[{Cos[t], Sin[t], t}, {t, 0, 2 Pi}]'
2*Sqrt[2]*Pi

Unbounded regions have infinite length.

$ wo 'ArcLength[HalfLine[{0, 0}, {1, 1}]]'
Infinity