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Math Help - stokes theorem

  1. #1
    Super Member
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    stokes theorem

    may i know what mistake have i made?

    given that the vector field F(x,y,z) = < -y,x,x-2y>. use stokes theorem to compute the upward flux of curl F across z=1-x^2 -y^2 with z>0.

    what i did:

    curl F =<-2,-1,2>

    using stoke theorem, integral F. dr = double integral curl F dS = triple integral grad (Curl F) dxdydz =0 as grad (curl F)=0


    may i know why this doesnt work?

    thanks!
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  2. #2
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    using stoke theorem, integral F. dr = double integral curl F dS
    this integral is along the closed curve dr, dS boundary is the closed curve dr.
    dS may be arbitrary. (there is no volume)

    double integral curl F dS = triple integral grad (Curl F) dxdydz =0
    this integral is along volume dxdydz and surfase dS surounds this all volume.
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  3. #3
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    does that mean that i cant convert it to triple integral because there is no volume?

    sorry im still abit lost about why i cant convert it from double to triple integral. could you explain it to me again?

    then when would i know when i can convert from single to double integrals and then from double to triple and when i should not convert ?

    thanks so much for your help
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  4. #4
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    You can't convert it to a triple integral because Stoke's theorem says nothing about triple integrals! Stoke's theorem says that a certain integral over a surface is equal to another integral around the boundary of that surface.
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