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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!

    (I know I double posted- could someone please delete the thread in the urgent homework section? Thank you!)
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  2. #2
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    Quote Originally Posted by hottytoddychick View Post
    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!

    (I know I double posted- could someone please delete the thread in the urgent homework section? Thank you!)
    The line element:

    ds = (1+|dy/dx| ^2 )^{1/2} dx = (1+x^2)^{1/2} dx

    Then:

    int_S f(x,y) ds=int_{x=0 to 2} (2x) (1+x^2)^{1/2} dx

    RonL
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  3. #3
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    I'm supposed to do a parametrisation to get the integral, and for the answer I got from working out what you gave me, I have (5root5)/10. The answer in the back of the book is (10root5 - 2)/3
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by hottytoddychick View Post
    I'm supposed to do a parametrisation to get the integral, and for the answer I got from working out what you gave me, I have (5root5)/10. The answer in the back of the book is (10root5 - 2)/3
    The parameterisation is t=x, and check your integration, QuickMath gives the answer from the back of your book.

    RonL
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