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U sub help

  1. Aug 26, 2009 #1
    1. The problem statement, all variables and given/known data
    I'm trying to find the arc length of a curve over an interval and I've arrived at
    [tex]\int[/tex] (y4 +2y2 +1)1/2 dy
    and now I'm pretty sure i should use a u substitution in order to integrate.
    I tried using u=y2 so du=2y dy so dy=du/2y
    Then you have [tex]\int[/tex] (u2+2u+1)1/2 and eventually it boils down to [tex]\int[/tex] u+1 du which gives you u2/2 +u

    But I think I forgot to incorporate the du/2y and I don't know if I can just change the answer to y2/2 + y.

    Any thoughts?
    Last edited: Aug 26, 2009
  2. jcsd
  3. Aug 26, 2009 #2


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    Homework Helper

    You don't have to 'u sub' anything yet. First try and simplify (y^4+2*y^2+1)^(1/2). Isn't y^4+2*y^2+1=(y^2+1)^2? What's the (1/2) power of that?
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