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Arc length and surfaces

  1. Feb 9, 2009 #1






    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Feb 9, 2009 #2


    Staff: Mentor

    What, are we supposed to guess what the problem is from the title on the thread? Presumably you want to find the arc length along the curve between points A and B.

    What does this have to do with surfaces, though?

    For the arc length, the integrand is sqrt(1 + (y')^2), which can be written as
    [tex]\sqrt{1 + (\frac{x^2}{4} - \frac{1}{x^2})^2}[/tex]
    [tex]=\sqrt{1 + \frac{x^4}{16} -1/2 + \frac{1}{x^4}}[/tex]

    The last three terms under the radical are a perfect square. When you add the first term, you'll still have a perfect square, which makes it easy to take the square root, which means you'll have an easy function to integrate.
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