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Math Help - Line integral

  1. #1
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    Line integral

    Hey i am working on problem number 1 here, and showed that it is a conservative vector just fine. However, when i solve for the integrand using f(c(t)) dot c'(t), I get an extremely long polynomial over a fraction, and taking the integral of this seems kind of unreasonable, especially since we are not allowed calculators. The integral is :
    (-2t(3t16 - 9t13 - t11 + 12t10 +8t8 -2t6 -14t5 -3t4 +t3 +3t +2))/(t12 -2t7 +t2 +1)2
    I did the integral on wolfram and got -1, but i feel like i am doing something wrong.
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  2. #2
    Senior Member jakncoke's Avatar
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    Re: Line integral

    how did you show it was a conservative vector field. Use this fact,

    if \nabla G = F then  \int_{C} F dr = G(b) - G(a)
    Last edited by jakncoke; February 20th 2013 at 03:18 PM.
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  3. #3
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    Re: Line integral

    Oh wow thanks alot im an idiot...
    I showed it was conservative by taking the partial derivatives of the x component of the vector in terms of y, then taking the partial deriv of the y component in terms of x and checking if they were equal to each other, which they were.
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  4. #4
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    Re: Line integral

    For the second problem, in order to find the normal vector I would take the partial derivs of G(theta, phi) in terms of theta and phi, then take the cross product correct? If so, what are the bounds for?
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