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Homework Help: Find the arc length parametrization of a curve

  1. Oct 15, 2014 #1
    1. The problem statement, all variables and given/known data
    Find the arc length parametrization of the curve r = (3t cost, 3tsint, 2sqrt(2)t^(3/2) ) .

    2. Relevant equations
    s(t)=integral of |r'(t)| dt

    3. The attempt at a solution
    I was able to get the integral of the magnitude of the velocity vector to simplify to:
    s(t) = integral of sqrt(9(1+t)^2) dt
    evaluating the integral, s(t) = 3t+(3/2)t^2
    In other problems similar to this one I would solve for t in terms of s then put it back into the original equation, but for this one I was unable to solve for t in terms of s.
  2. jcsd
  3. Oct 15, 2014 #2


    User Avatar
    Science Advisor
    Homework Helper

    I don't see the problem in solving for t. It's just a quadratic equation.
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