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Surface integral question

Hey, I think the question is asking for a surface integral or maybe asking for you to use the divergence theorem but... does anybody have an idea of how to solve this problem?

(It's not coursework or anything, simply a past paper where the answer is -22.5)

"Evaluate Fndo\int \int F \cdot n do where y2i(x+2z)j+yzky^2i-(x+2z)j+yzk, S is the surface of the plane x+2y+2z=6 in the first octant, and n is the unit normal to the surface."

Any ideas?
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Original post by BirdieUK
Hey, I think the question is asking for a surface integral or maybe asking for you to use the divergence theorem but... does anybody have an idea of how to solve this problem?

(It's not coursework or anything, simply a past paper where the answer is -22.5)

"Evaluate Fndo\int \int F \cdot n do where y2i(x+2z)j+yzky^2i-(x+2z)j+yzk, S is the surface of the plane x+2y+2z=6 in the first octant, and n is the unit normal to the surface."

Any ideas?


First parametrize the equation of the plane with f.e. u and v
x=u y=v z=6-2u-2v
The vector field:
F=v2i+(3u+4v12)j+(6v2uv2v2)kF=v^2\vec{i}+(3u+4v-12)\vec{j}+(6v-2uv-2v^2)\vec{k}

The normal to the surface vill be the n=ru\vec{n}=\frac{ \partial \vec{r}}{\partial u} x rv\frac{\partial \vec{r}}{\partial v}
Calculate the cross product, then integrate the dot product of F and n by dudv
(edited 13 years ago)

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