What is wrong with my calculating in this determinant? (Stokes theorem)

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The task is: "Let $gamma$ be the cutting curve between the surface $$z=sqrt2(x^2+y^2)$$ and the plane $$z=x+1$$ orienteted opposite the clock - looking upwards. So $$F(x,y,z)=(y^2,2yz,-xy)$$ Calculate $$int_gamma F cdot dr$$



I have trouble to get the right curl F here. I set it up like this (see the picture) :



curlF



and i also trying to find the normal with this: $$N = (-z'_x , -z'_y , 1) $$



where i look at the F function and I get $$N=(0,2,1) which is wrong.



Can someone help me out? :s




curl




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    up vote
    0
    down vote

    favorite












    The task is: "Let $gamma$ be the cutting curve between the surface $$z=sqrt2(x^2+y^2)$$ and the plane $$z=x+1$$ orienteted opposite the clock - looking upwards. So $$F(x,y,z)=(y^2,2yz,-xy)$$ Calculate $$int_gamma F cdot dr$$



    I have trouble to get the right curl F here. I set it up like this (see the picture) :



    curlF



    and i also trying to find the normal with this: $$N = (-z'_x , -z'_y , 1) $$



    where i look at the F function and I get $$N=(0,2,1) which is wrong.



    Can someone help me out? :s




    curl




    share|cite|improve this question
























      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      The task is: "Let $gamma$ be the cutting curve between the surface $$z=sqrt2(x^2+y^2)$$ and the plane $$z=x+1$$ orienteted opposite the clock - looking upwards. So $$F(x,y,z)=(y^2,2yz,-xy)$$ Calculate $$int_gamma F cdot dr$$



      I have trouble to get the right curl F here. I set it up like this (see the picture) :



      curlF



      and i also trying to find the normal with this: $$N = (-z'_x , -z'_y , 1) $$



      where i look at the F function and I get $$N=(0,2,1) which is wrong.



      Can someone help me out? :s




      curl




      share|cite|improve this question














      The task is: "Let $gamma$ be the cutting curve between the surface $$z=sqrt2(x^2+y^2)$$ and the plane $$z=x+1$$ orienteted opposite the clock - looking upwards. So $$F(x,y,z)=(y^2,2yz,-xy)$$ Calculate $$int_gamma F cdot dr$$



      I have trouble to get the right curl F here. I set it up like this (see the picture) :



      curlF



      and i also trying to find the normal with this: $$N = (-z'_x , -z'_y , 1) $$



      where i look at the F function and I get $$N=(0,2,1) which is wrong.



      Can someone help me out? :s





      curl





      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited Aug 16 at 8:06









      Riemann

      2,4811219




      2,4811219










      asked Aug 16 at 7:58









      soetirl13

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