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Finding Arc Length

  1. Jun 21, 2011 #1
    1. The problem statement, all variables and given/known data

    Determine the arc length of the function on the given interval

    x = (y^4)/8 + 1/(4y^2) from 1 to 2

    The arc length formula

    [itex]\int[/itex] (f'(x)2 + 1).5 dx

    3. The attempt at a solution

    I used the arc length formula but don't know where to go from here. Usually these problems can't be done unless a form of cancellation takes place and I can't seem to find it. Below is what I input in the formula but I can not figure out how to integrate this.

    [itex]\int[/itex]((y6 - 1)2/(2y3)) + 1))).5 dy
  2. jcsd
  3. Jun 21, 2011 #2


    Staff: Mentor

    It's helpful in this problem to use negative exponents instead of fractions.

    (x')2 + 1 = (1/4)y6 - 1/2 + (1/4)y-6 + 1
    = (1/4)y6 + 1/2 + (1/4)y-6

    This turns out to be a perfect square, so you can readily take its square root.
  4. Jun 21, 2011 #3
    I factored and then took the square root and came up with this:

    (y^3)/2 + 1/2y^3
  5. Jun 22, 2011 #4


    User Avatar
    Science Advisor

    Yes, that is correct. Now integrate.
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