NOTE 1 For a curve from A to B defined by the position vector $r=f(u)$ as a function of the parameter u in the given interval [a, b] where $a\le b$, the length of the curve is the line integral ${\displaystyle \underset{\text{A}}{\overset{\text{B}}{\int }}\left|\mathrm{d}r\right|}={\displaystyle \underset{a}{\overset{b}{\int }}\left|\frac{\mathrm{d}f}{\mathrm{d}u}\right|\mathrm{d}u}$.

NOTE 2 In the usual geometrical space, the length of a curve is a quantity of the dimension length.