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Arc Length/Help with Integral

  1. Sep 5, 2011 #1
    1. The problem statement, all variables and given/known data
    [tex]y=\frac{1}{3}\left(x^2+2\right)^{3/2}[/tex]


    2. Relevant equations
    [tex]\int_{a}^{b}\sqrt{1+\left(\frac{dy}{dx}\right)^{2}}dx[/tex]


    3. The attempt at a solution
    [tex]\frac{dy}{dx}=x\sqrt{x^2+2}[/tex]
    [tex]\int_{0}^{3}\sqrt{1+\left(x\sqrt{x^2+2}\right)^{2}}dx=\int_{0}^{3}\sqrt{1+x^4+2x^2}dx[/tex]
    I'm stuck with that integral, not sure what the antiderivative for that function would be
    Any hints at the next step would be greatly appreciated.
     
  2. jcsd
  3. Sep 5, 2011 #2

    Char. Limit

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    Gold Member

    Here's a hint: x4+2x2+1 = (x2+1)2
     
  4. Sep 5, 2011 #3
    Wow I can't believe i didn't see that.
    I tried Wolfram Alpha earlier and they used a substitution but i couldn't follow their steps so i decided to consult the Physics Forums.
    Thanks Char. Limit.
     
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