F = 5xi + 5yj + 6zk and $\sigma$ is the portion of the cone $z = \sqrt{x^2 + y^2}$ between the planes $z = 1$ and $z = 8$ oriented with normal vectors pointing upwards. Find the flux of the flow field F across $\sigma$.
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Step 1: The flux of the flow field F across the surface $\sigma$ is given by the surface integral $$ \iint_{\sigma} \mathbf{F} \cdot d\mathbf{S} $$ where $d\mathbf{S} = \mathbf{n} dS$ is the vector surface element, and $\mathbf{n}$ is the unit normal vector to the Show more…
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