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Math Help - Final in 6 hours! Line Integrals!

  1. #1
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    Final in 6 hours! Line Integrals!

    My final is in 6 hours. I've been slowly teaching myself line integrals and I'm stumped. Here's the problem:

    Integrate f over the given curve:

    f (x,y) = x3/y
    C: y = x2/2
    0<= x <= 2

    I don't even know where to start! There's no example like this in the text. I have nothing to follow.

    I know I need r(t), |v(t)|, and an interval for t, but I'm completely clueless!
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  2. #2
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    parametrization

    The parametrization you need to perform is : x=t, y=t^2/2, where 0<t<2.
    The function f(x,y) becomes f(t) : x^3/y=t^3/(t^2/2)=2t. The integral
    gives t^2 (from 0 to 2) =4.
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