[See Steps] Let the surface S be the part of the cone z=√x^2+y^2 that lies in the region 0≤ z≤ 2. Let F(x, y, z) be the vector field F(x,y,z)=xzi+yzj+zk
Question: Let the surface S be the part of the cone \(z=\sqrt{{{x}^{2}}+{{y}^{2}}}\) that lies in the region \(0\le z\le 2\). Let F(x, y, z) be the vector field
\[\vec{F}\left( x,y,z \right)=xz\mathbf{i}+yz\mathbf{j}+z\mathbf{k}\]Calculate the flux integral
\[\iint\limits_{S}{\vec{F}\cdot \vec{n}dS}\]where n is the outward pointing unit normal on S.
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