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**Markov** Let $\displaystyle S$ the surface $\displaystyle x^2+y^2-(z-6)^2=0$ for $\displaystyle 3\le z\le 6.$ Graph $\displaystyle S$ and graphically indicate an orientation for $\displaystyle S$ and compute the whole flux through $\displaystyle S$ of the field $\displaystyle \bold F(x,y,z)=(x(3-z),y(3-z),(3-z)^2).$

I can apply the divergence theorem but I'm struggled with the bounds, I don't know the triple integral should look like.

How can be done by using a line integral? I'd have to parametrize the surface, but I'd like to know how to set up the integral!

Any help will be appreciated!