Dear Folks,

Glad to see good old MHF forum back :-)

Suppose that $\displaystyle \vec r(t)$ is a parameterised curve defined for $\displaystyle a \le t\le b$ and

$\displaystyle \displaystyle s(t)=\int_{a}^{t}\left \| d \vec r (t) \right \|dt$ is the arc length function measured from r(a)

a) Prove that s'(t) = || dr(t)||

How do I start this? It is easy to see that differentiating both sides will yield the proof but I dont know how to go about t. Any clues?

I tried something like letting r(t) = (t,f(t)) where x=t. Then $\displaystyle \left \| d\vec r(t) \right \|=\sqrt{1+ (f'(t)^2)}$................?

Note I have this posted at the sister site. I will keep both forums updated to ensure no ones time is wasted. Thanks

Parameterised Curve Proof Part 1