Definition:Arc Length of Regular Curve/3-Dimensional Real Vector Space

Definition
Let $\alpha : I \to \R^3$ be a regular curve.

Let $t_0 \in I$.

Then the arc length of $\alpha$ from $t_0$ is defined as:
 * $\ds \map s t := \int_{t_0}^t \norm {\map {\alpha '} t} \rd t$

where:
 * $\alpha '$ denotes the derivative of $\alpha$
 * $\norm \cdot$ denotes the Euclidean norm on $\R^3$