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Solving length of the curve

  1. Sep 20, 2009 #1
    The problem statement, all variables and given/known data

    Find the length of the curve x^(2/3)+y^(2/3) = 1 for x in the interval [0.1].

    The attempt at a solution

    y = (1-x)^(2/3)
    f'(x) = (4x^(-1/3) (1-x^(2/3))^(1/2))/9

    then i plugged it into arc length formula
    1
    S sqrt(1+((4x^(-1/3) (1-x^(2/3))^(1/2))/9)^2 =
    0

    1
    S sqrt(1+((16x^(-2/3) (1-x^(2/3))/81) =
    0

    1
    S sqrt(1+((16x^(-2/3) -16)/81) =
    0

    1
    S sqrt(16x^(-2/3) +65))/81 =
    0

    '''''''''1
    1/9 S sqrt(16x^(-2/3) +65) = ...
    '''''''''0

    then I got stuck.. I wasn't even sure if I was solving this question the right way.
    If I let u = (16x^(-2/3) +65), then whole bunch of weird numbers come out..

    thank you in advance
     
  2. jcsd
  3. Sep 20, 2009 #2
    You started with the wrong equation for y. Exponents are wrong or missing.
     
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