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Line integral problem

  1. Oct 20, 2010 #1
    1. The problem statement, all variables and given/known data

    Evaluate the following line integral on the indicated curve C

    [tex]\int(y^2-x^2)ds[/tex]

    C: x = 3t(1+t), y=t^3 ; 0 <= t <= 2



    2. Relevant equations

    ds = [tex]\sqrt{(f'(t))^2+(g'(t))^2}dt[/tex]

    3. The attempt at a solution

    dx/dt = 3+6t
    dy/dt = 3t^2

    ds = [tex]\sqrt{(3+6t)^2+(3t^2)^2}[/tex]dt
    ds = 3*[tex]\sqrt{t^4+4t^2+4t+1}[/tex]dt

    y^2 = t^6
    x^2 = (3t+3t^2)^2 = 9t^2+18t^3+9t^4

    [tex]\int(y^2-x^2)ds = 3\int(t^6-9t^2-18t^3-9t^4)\sqrt{t^4+4t^2+4t+1}dt[/tex]

    From here I don't know how to solve the integral, and it looks way more complicated than what we have done so far in class. Maybe I am doing something wrong? Or there is a trick involved here? Any help would be greatly appreciated. Thanks.
     
    Last edited: Oct 21, 2010
  2. jcsd
  3. Oct 20, 2010 #2

    Mark44

    Staff: Mentor

    I see a typo, but I can't offer any more help than that.
    [tex]\int(y^2-x^2)ds = 3\int(t^6 -9t^2-18t^3-9t^4)\sqrt{t^4+4t^2+4t+1}dt[/tex]
     
  4. Oct 21, 2010 #3
    Thanks Mark44, I corrected the mistake in the first post. I will come back to this thread if I find an answer and post it.
     
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