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Calculating Arc Length

  1. Aug 1, 2010 #1
    I need to find the arc length of the function f(x) = 4/5*X5/4 from [0,4].

    You have to find f '(x) first and that would be X1/4

    I square f '(x) and obtain X1/2 or [tex]\sqrt{X}[/tex]

    I plug it into the formula and get

    S = [tex]\int[/tex][tex]\sqrt{1+\sqrt{X}}[/tex] from [0,4]

    I don't know how to evaluate the integral from here though
     
  2. jcsd
  3. Aug 1, 2010 #2

    vela

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    Don't forget the dx. Try a u-substitution or two.
     
  4. Aug 1, 2010 #3
    Imagine a right triangle with the two legs as 1 and [tex] x^{1/4}. [/tex] Let [tex] \theta
    [/tex] be the angle opposite [tex] x^{1/4}. [/tex]

    Use this to put [tex] \sqrt{1 + \sqrt{x} } [/tex] and [tex] dx [/tex] in terms of [tex] \theta [/tex] by using some trig operations. Can you get the rest from here?
     
  5. Aug 2, 2010 #4

    vela

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    There's really no reason to resort to a trig substitution. There are a couple of obvious substitutions to try, and they will result in a integrand that's straightforward to integrate.
     
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