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Math Help - Evaluate line integral (parabola)

  1. #1
    Member mybrohshi5's Avatar
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    Evaluate line integral (parabola)

    Evaluate the line integral \int^._c F \cdot dr
    where C is the portion of the parabola y = x^2 from (0,0) to (1,1) if  F(x,y) = <3ye^{xy}, 3x^2>

    This is what i get. Can anyone check this for me please thanks!

     c: r(t) = <t,t^2> where 0 < t < 1

     \frac{dr}{dt} = <1,2t>

    F(r(t)) = <3te^t^3, 3t^2>

    F(r(t)) \cdot \frac{dr}{dt} = <3t^2e^t^3, 3t^2> \cdot <1,2t> = 3t^2e^t^3 + 6t^3

    \int_0^1 3t^2e^t^3dt + \int_0^1 6t^3dt

    (e-1) + \frac{3}{2} = e + \frac{1}{2}

    Thanks for looking over this
    Last edited by mybrohshi5; December 4th 2010 at 09:20 PM.
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  2. #2
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    This is right. You just made a little mistake in the first component of F(r(t)). It has a factor of t^2 (not t). You actually corrected this later on, so your answer is correct.

    Also, it should be dr/dt (not just dr).
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  3. #3
    Member mybrohshi5's Avatar
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    Thank you. Changes were corrected in post
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