Arc Length of a Curve
The length of a curve or line.
The length of an arc can be found by one of the formulas below for any differentiable curve defined by rectangular, polar, or parametricequations.
For the length of a circular arc, see arc of a circle.
 
where a and b represent x, y, t, or θvalues as appropriate, and ds can be found as follows. 1. In rectangular form, use whichever of the following is easier: 2. In parametric form, use 3. In polar form, use
 
Example 1: Rectangular  Find the length of an arc of the curve 
 
Example 2: Parametric  Find the length of the arc in one period of the cycloid

Example 3: Polar  Find the length of the first rotation of the logarithmic spiral 
See also
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