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Math Help - vector field integrals

  1. #1
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    Question vector field integrals

    Question

    Let S be the disk { (x,y,z) such that (x-1)^2 +(z-2)^2 =9 , y=17}, and let C be the boundary of S oriented counterclockwise if viewed from the top of the positive y-axis. Suppose F(x,y,z)= f(x,y,z)i + g(x,y,z)j + h(x,y,z)k, where f and g and h have continuous first partial. Also assume fsubz=hsubx
    thoughout some open set containing S.
    Prove that the integral of C (closed) F dot T ds =0.

    Thank you
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  2. #2
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    can someone help me this question??? its urgent. Thanks
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by universe09 View Post
    Question

    Let S be the disk { (x,y,z) such that (x-1)^2 +(z-2)^2 =9 , y=17}, and let C be the boundary of S oriented counterclockwise if viewed from the top of the positive y-axis. Suppose F(x,y,z)= f(x,y,z)i + g(x,y,z)j + h(x,y,z)k, where f and g and h have continuous first partial. Also assume fsubz=hsubx
    thoughout some open set containing S.
    Prove that the integral of C (closed) F dot T ds =0.

    Thank you
    what about gsuby?

    the idea here, i think, is to use this to show that F is a conservative vector field. and since its components have continuous partial derivatives on an open set containing C, we know that we have

    \oint_C \bold{F} \cdot \bold{T}~ds = \oint_C \bold{F} \cdot d \bold{r} = 0
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