Parameterization by arc length is a method to parameterize a curve such that the resulting function has the parameter such that is the arc length of the original curve.

To parameterize a curve by arc length first the curve needs to be parameterized normally into some function , then using the equation for arc length we solve for giving us some function which gives us a function which is our curve parameterized by arc length.

Example

Re-parameterize the function in terms of arc length measured from .