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Thread: Line Integral help!

  1. #1
    Newbie TheTideCaller's Avatar
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    Line Integral help!

    Hey all, I'm stuck in having to do a problem on my homework. It goes like this...

    F(x,y) = <-y, x>, r(t) is the graph y = x^2 from (0,0) to (3,9).

    My best guess right now is having the bounds of said integral from 0 to 3. Besides that, I do not know what to do to start setting this up. Any help to get me started on it? I'm trying to evaluate the line integral, nothing in my notes has a problem looking like this.
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  2. #2
    MHF Contributor
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    Re: Line Integral help!

    I'm not entirely sure what the problem is but it looks like

    $r(t) =(t, t^2),~t \in [0,3]$

    $dr = (1,2t)~dt$

    $F(x,y) = (-y,x) = (-t^2, t)$

    $F\cdot dr = (-t^2 + 2t^2) ~dt = t^2~dt$

    $\ell = \displaystyle \int_C F\cdot dr = \int_0^3~t^2~dt = \left . \dfrac{t^3}{3}\right|_0^3 = 9$
    Last edited by romsek; Apr 17th 2017 at 06:38 PM.
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  3. #3
    Newbie TheTideCaller's Avatar
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    Re: Line Integral help!

    Oh my god it's correct! Now it looks simple enough, I had no idea how it was supposed to be set up or how to make the parameters made. Thanks so much!
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