(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Evaluate the surface Integral [tex]I=\int\int_S\vec{F}\cdot\vec{n}\,dS[/tex]

where [tex]\vec{F}=<z^2+xy^2,x^100e^x, y+x^2z>[/tex]

and S is the surface bounded by the paraboloid [itex]z=x^2+y^2[/itex]

and the plane z=1; oriented by the outward normal.

3. The attempt at a solution

[tex]I=int\int_S\vec{F}\cdot\vec{n}\,dS=\int\int\int_E(div\vec{F})dV[/tex]

[tex](div\vec{F})=y^2+x^2[/tex]

[tex]\Rightarrow I=\int\int_D(\int_{z=x^2+y^2}^1(x^2+y^2)\,dz)\,dA[/tex]

[tex]\Rightarrow I=\int\int_D(1-(x^2+y^2)\,dA[/tex]

Is it just Polar Coordinates all the way home now?

Thanks,

Casey

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# Homework Help: Surface Integral using Divergence Theorem

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