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Math Help - Help with Stokes Theorem

  1. #1
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    Help with Stokes Theorem

    The question states: F(x,y,z)=(y-z, 7z-8, x-7y). Compute line integral F.ds along the unit circle c(t)=(cos(t), sin(t), 0), 0<=t<=2pi.

    So by doing the line integral F(c(t)).c'(t) you get -2pi. But how do you go about it using Stokes Theorem? What is the parametrization and what form of it would you use? Curl of F.dS?
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    Quote Originally Posted by arperidot View Post
    The question states: F(x,y,z)=(y-z, 7z-8, x-7y). Compute line integral F.ds along the unit circle c(t)=(cos(t), sin(t), 0), 0<=t<=2pi.

    So by doing the line integral F(c(t)).c'(t) you get -2pi. But how do you go about it using Stokes Theorem? What is the parametrization and what form of it would you use? Curl of F.dS?
    You cannot do this with Stoke's theorem. Because Stoke's theorem is computing surface integrals,
    you are asking a question about computing line integrals.
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  3. #3
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    Quote Originally Posted by ThePerfectHacker View Post
    You cannot do this with Stoke's theorem. Because Stoke's theorem is computing surface integrals,
    you are asking a question about computing line integrals.
    Actually you can. The surface is z = 0, x^2+y^2 \le 1

     <br />
\nabla \times F = < -14,-2, -1> <br />

    and

    \vec{n} = <0,0,1> so \nabla \times F \cdot \vec{n} = -1

    Thus

     <br />
\iint_R \nabla \times F \cdot \vec{n} dS = -\iint_R 1 dA = -2 \pi<br />
noting that since z = 0, dA = dx dy = r dr d \theta
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