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Find the length of the curve given by the parametric representation

  1. Nov 20, 2011 #1
    Find the length of the curve given by the parametric representation....

    1. The problem statement, all variables and given/known data
    Calculate the length of the curve given by the parametric representation
    r(t) = t2(cos t; sin t; cos 2t; sin 2t) for 1≤ t ≤+1:


    2. Relevant equations



    3. The attempt at a solution

    I know that you need to assume: dx/dt ≥ 0 for α≤t≤β

    Then you use the formula for 'L'

    Imstruggling with the layout of the question.. Why are there semi-colons between the sin and cos terms?

    If someone could explain this that would be great.

    Regards as always.
     
  2. jcsd
  3. Nov 20, 2011 #2
    Re: Find the length of the curve given by the parametric representation....

    There are probably semi-colons to distinguish between the four different dimensions. So x(t) = t^2 cos(t), y(t) = t^2 sint, etc.
     
  4. Nov 21, 2011 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Re: Find the length of the curve given by the parametric representation....

    I presume you know that the length of the curve given by r(t), from t= a to t= b, is
    [tex]\int_a^b ||r'(t)|| dt[/tex]
    where r'(t) is the tangent vector and the || || is the length of that vector.
     
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