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Arc Length/Help with Integral

  • Thread starter miglo
  • Start date
97
0
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.
 

Char. Limit

Gold Member
1,198
12
Here's a hint: x4+2x2+1 = (x2+1)2
 
97
0
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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