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Math Help - Find curves C1 and C2 that are not closed

  1. #1
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    Find curves C1 and C2 that are not closed

    f = grad, where (x,y)=sin(x-2y)

    Find curves C1 and C2 that are not closed and satisfy the equations

    i) ∫C1 Fdr = 0

    ii) ∫C2 Fdr = 1
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  2. #2
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    Quote Originally Posted by enterprise-solutions View Post
    f = gradƒ, where ƒ(x,y)=sin(x-2y)

    Find curves C1 and C2 that are not closed and satisfy the equations

    i) ∫C1 F•dr = 0

    ii) ∫C2 F•dr = 1

    1) for the first one since we want the integral equal to zero, The sine function equals zero when its argument is zero so set

    x+2y=0 and we get..

    y=-\frac{x}{2}

    so any curve on that path will give an integral of zero.

    for #2

    using the fundemental theorem for line integrals

     \int_c= \overrightarrow{F} \cdot d \overrightarrow{r}=\nabla{f(r_2)}- \nabla{f(r_1)}

    so we need to pick a path that the difference of it's end point is 1.

    so try

     (\frac{\pi}{2},0) \mbox{and} (0,0)
    Last edited by TheEmptySet; March 18th 2008 at 08:04 AM. Reason: I don't know how to read.
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