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Lengths of parametric curves

  1. Feb 4, 2012 #1
    1. The problem statement, all variables and given/known data

    x = t^3, y = (3t^2)/2 0<= t <= √3

    3. The attempt at a solution

    dx/dt = 3t^2
    dy/dt = 3t

    step 1. √((3t^2)^2 + (3t)^2)

    step 2. 3t^2 + 3t

    (the book says I can't do that, I don't see why)

    step 3. insert √3 into t

    Here's the books solution


    I understand u substitution but I don't see why it's necessary here. I don't why my method does not follow all the rules.
  2. jcsd
  3. Feb 4, 2012 #2


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    Because ##\sqrt{a^2+b^2} \ne a+b##. Try it with a=b=1, for instance.
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