\begin{definition}[Definition:Arc Length]
Let $y = \map f x$ be a real function which is:
:continuous on the closed interval $\closedint a b$
and:
:continuously differentiable on the open interval $\openint a b$.
The '''arc length''' $s$ of $f$ between $a$ and $b$ is defined as: 
:$\ds s := \int_a^b \sqrt {1 + \paren {\frac {\d y} {\d x} }^2} \rd x$
\end{definition}