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I'm struggling to compute arc length (multivariable calculus)

  1. Apr 28, 2013 #1
    1. The problem statement, all variables and given/known data
    Find the arc length of the curve
    (t) = (1; 3t2; t3) over the interval 0  t  1.

    2. Relevant equations
    L=sqrt(f'(t)^2+g'(t)^2+.....+n'(t)^2) (integrated from a to b)
    int(udv)=uv-int(vdu)


    3. The attempt at a solution
    Seems like it should be fairly straightforward-- the derivative vector ends up being (0, 6t, 3t^2)
    1.) L=int[sqrt(0^2+(6t)^2+(3t^2)^2)] (over 0 to 1)
    2.) L=int[sqrt(36t^2+9t^4)] (from 0 to 1)
    3.) L=3int[t*sqrt(t^2+4)] (from 0 to 1)
    4.) From here, I wanted to solve using integration by parts. However, that seemed to only result in a more complicated integral no matter whether I set t as u or as dv.

    Can anyone give me a hint? I'd like to work it out on my own, but an idea as to which method to use would be much appreciated.
    Thanks so much to anyone who takes the time to respond to this. :)
     
  2. jcsd
  3. Apr 28, 2013 #2

    ehild

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    Us integration by substitution. Is not the factor t connected to the derivative of t2+4?

    ehild
     
  4. Apr 28, 2013 #3
    Thank you!!
     
  5. Apr 28, 2013 #4
    Can't believe I missed that...
     
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