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Finding the length of a graph

  1. Sep 21, 2008 #1
    1. The problem statement, all variables and given/known data
    Determine the length of the following graph:

    [tex]f(x) \ = \ \frac{x^5}{10} + \frac{1}{6x^3}[/tex]

    2. Relevant equations

    length of a graph: [tex]\int \sqrt{1 + f'(x)^2}dx[/tex]

    3. The attempt at a solution

    so [tex]f'(x) = \frac{x^4}{2} -\frac{1}{18x^4} [/tex]

    [tex]f'(x)^2 = \frac{x^8}{4} + \frac{1}{18} + \frac{1}{324x^8}[/tex]

    Is f'(x)^2 correct?

    Did I even need to expand, or is there some trick to this?
  2. jcsd
  3. Sep 21, 2008 #2


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    There is almost always a trick to length of arc problems and the trick is almost always make the expression under the radical into a perfect square. Add 1 to f'^2 and you will see that you can. Except fix f'(x) first. I get x^4/2-1/(2*x^4). Why don't you?
    Last edited: Sep 21, 2008
  4. Sep 21, 2008 #3
    I see what I did wrong. I "brought up" the 6 as well, so I wrote it as 6x^-3
  5. Sep 21, 2008 #4


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    Ok, so can you square it and then express the expression under the radical as a perfect square? I'm betting you can.
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