f=(x/a)^2+(y/b)^2+(z/c)^2(adsbygoogle = window.adsbygoogle || []).push({});

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:

(x/a)^2+(y/b)^2+(z/c)^2=1

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)*G)grad(f)=

4(1/d+1)[x^2/(a^2)+y^2/(b^2)+z^2/(c^2)])(x/(a^2),y/(b^2),z/(c^2))

|grad(f)|^2 G - (grad(f) * G)grad(f)=

4(1/d+1)*

{[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

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# Plane integral(type2) exer

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