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Plane integral(type2) exer

  1. Sep 13, 2004 #1


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    G=(x/d+x,y/d+y,z/d+z) while d=(x^2+y^2+z^2)^(3/2)

    how can i calculate value of
    I=SS { |grad(f)|^2 G - (grad(f) * G)grad(f) } dS
    when the area is S:
    and normal vector to S is pointed to (0,0,0)

    some calculations i did :

    grad (f)=( 2x/(a^2) , 2y/(b^2) , 2z/(c^2) )

    |grad (f)|^2= 4x^2/(a^4) + 4y^2/(b^4) + 4z^2/(c^4)

    |grad(f)|^2 G=4(1/d+1)*[x^2/(a^4) + y^2/(b^4) + z^2/(c^4)] (x,y,z)

    grad(f) * G= 2(1/d+1)[x^2/(a^2) + y^2/(b^2) + z^2/(c^2)]


    |grad(f)|^2 G - (grad(f) * G)grad(f)=
    {[x^2/(a^4) + y^2/(b^4) + z^2/(c^4)] (x,y,z) -
    [x^2/(a^2)+y^2/(b^2)+z^2/(c^2)] (x/(a^2),y/(b^2),z/(c^2))}

    i guess im not at the right way..

    plz help

    thank you
  2. jcsd
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