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Find the arc length of f(x) (x^(5/4))/5

  1. May 16, 2010 #1
    1. The problem statement, all variables and given/known data

    find the arc length of f(x) (x^(5/4))/5.
    The integration limits are from 0 to 4.

    2. Relevant equations

    The arc length formula is integrate sqrt(1 + (f'(x))^2)

    3. The attempt at a solution

    f'(x) = (5/4)*(1/5)*x^(1/4) = x^(1/4)/4

    integral of sqrt(1 + (x^(1/4)/4)^2) = integral of sqrt(1 + sqrt(x)/16)

    The part I am stuck on is getting rid of either sqrt roots.

    Ive tried this: integral of sqrt(sqrt(x)/sqrt(x)/ + x/(sqrt(x)16))
    but that didnt get me any where....Any idea how to simplify this? Im thinking that there is some sort of algebraic simplification that I am missing.
  2. jcsd
  3. May 16, 2010 #2


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    Why not start by trying the substitution [tex]u=1+\frac{\sqrt{x}}{16}[/itex]?
  4. May 16, 2010 #3


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    Try letting x = u2 followed by v = 1 + (1/16)u.
  5. May 16, 2010 #4
    just make the integral like this >>> int of (1/4)Sqrt(16+ Sqrt(x)) dx

    then you can substitute >> u = 16 + sqrt(x)

    it'll be easy ;)
    Last edited: May 17, 2010
  6. May 17, 2010 #5
    Wow...what a novice mistake I made! Thanks!
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