The arc length is the distance between two points along a curve. Given a parameterized curve it's arc length from the point to is defined as follows:

Relation to Speed

In physical quantities if we consider the curve to be the position vector of a particle, it's derivative is therefore it's velocity, taking the size of this vector gives us the speed of the particle, the arc length is therefore just integrating the speed of a particle over time.

Examples

Find the arc length of one revolution of the helix for , where and are constants.