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Arc Length

  1. Feb 2, 2013 #1
    1. The problem statement, all variables and given/known data
    find the length of the following curve.


    2. Relevant equations
    y=(2/3)(x^2 +1)^(3/2) from x=3 to x=9.


    3. The attempt at a solution
    f'(x) = 2x^3 + 2x
    f'(x)^2 = 4x^6 + 8x^4 + 4x^2

    L = integral (3,9) sqrt(1+4x^6 + 8x^4 + 4x^2)
     
  2. jcsd
  3. Feb 2, 2013 #2

    tiny-tim

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    hi whatlifeform! :smile:
    no, you've got muddled :confused:

    try the chain rule again :smile:
     
  4. Feb 2, 2013 #3
    dy/dx = (2x) (x^2 + 1) ^ (1/2)
    (dy/dx)^2 = 4x^2 (x^2+1)

    L = integral (3,9) sqrt(1+4x^4 + 4x^2)
     
  5. Feb 2, 2013 #4

    haruspex

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    Yes. Can you see a simplification?
     
  6. Feb 3, 2013 #5

    tiny-tim

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    ie, what is √(4x4 + 4x2 + 1) ? :smile:
     
  7. Feb 3, 2013 #6
    take the integral of this?
     
  8. Feb 3, 2013 #7

    dx

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    Write the expression under the square-root as the square of something.
     
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