# Find the arc-distance between the start and end points of a Bézier curve

Given that I have the start, end and control points for a linear Bézier curve, I am trying to find the arc-distance between the start and end points. Google seems to be failing me this morning; can anyone point me in the right direction?

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If you have a parametric curve \begin{align*}x&=f(t)\\y&=g(t)\end{align*} for $a \leq t \leq b$, then the arclength you want is $\int_a^b \sqrt{f^\prime(t)^2+g^\prime(t)^2}\mathrm dt$. – J. M. Dec 31 '11 at 17:26
For the non-linear case, possible duplicate of math.stackexchange.com/questions/12186/… – lhf Dec 31 '11 at 20:49