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Help solving line integral question

  1. Jul 31, 2013 #1
    h1. The problem statement, all variables and given/known data

    Evaluate ∫xy|dr| over the path given by x=t^3, y=t^2, t=0...2

    2. Relevant equations

    x=t^3, y=t^2, t=0...2

    3. The attempt at a solution

    x=t^3, y=t^2
    y^(3/2) =x, y=t, x=t^(3/2), t=0...4
    ∫0to4 t^5/2 [Sqrt((3t^(1/2))/2)^2 +(1)^2]
    =∫0to4 t^5/2 [Sqrt(9t/4 + 1) dt

    HELP PLEASE, I'm not sure this is right. Help or point me in the right direction, would you? :-)
  2. jcsd
  3. Jul 31, 2013 #2


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    Homework Helper

    The usual notation for [itex]\|\mathrm{d}\mathbf{r}\|[/itex] is [itex]\mathrm{d}s[/itex].

    Your starting point is
    \int_C xy\,\mathrm{d}s =
    \int_0^2 x(t)y(t)\|\mathbf{r}'(t)\|\,\mathrm{d}t =
    \int_0^2 x(t)y(t)\sqrt{(x'(t))^2 + (y'(t))^2}\,\mathrm{d}t.

    Now substitute [itex]x(t) = t^3[/itex] and [itex]y(t) = t^2[/itex].
  4. Aug 1, 2013 #3
    My integral comes out to the same answer of 102.842 but your method seems a whole lot easier. I think I was just thinking too much about it. Thanks.
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