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Thread: Parameterised Curve Proof Part 1

  1. #1
    Senior Member bugatti79's Avatar
    Jul 2010

    Parameterised Curve Proof Part 1

    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
    Last edited by bugatti79; Nov 5th 2011 at 09:28 AM. Reason: Updating Post.
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