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Homework Help: Arc Length

  1. Feb 2, 2013 #1
    1. The problem statement, all variables and given/known data
    find the length of the curve.

    2. Relevant equations
    x=y^3/15 + 5/4y on 3<=y<=5

    3. The attempt at a solution
    (dy/dx)^2 = Y^4/25 - 1/2 + 25/16y^4

    integral (3,5) y^2/5 + 5/4y^2

    however, i got the wrong answer. the answer is 67/10.
  2. jcsd
  3. Feb 2, 2013 #2


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    Science Advisor
    Homework Helper
    Gold Member

    Is that 5/(4y) or (5/4)y. If you don't use Latex, at least use parentheses.

    That isn't (dy/dx)^2 although it may be (dx/dy)^2

    That isn't the right formula for arc length. You need$$
    \sqrt{1 + \left(\frac {dx}{dy}\right) ^2}\, dy$$in the integrand.
  4. Feb 2, 2013 #3
    ok so thus far this should be correct.

    L = integral (3,5) sqrt(1 + y^4/25 - 1/2 + 25/16y^4)

    this could be further simplified to: sqrt (y^2/5 + 5/4y^2)^2 --->

    y^3/15 - 5/4y ] (3 to 5)

    the answer is : 67/10 which i'm not getting.
  5. Feb 2, 2013 #4
    edit: solved.
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