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## Homework Statement

Let ##\mathit{F}(x,y,z) = (e^y\cos z, \sqrt{x^3 + 1}\sin z, x^2 + y^2 + 3)## and let ##S## be the graph of ##z = (1-x^2-y^2)e^{(1-x^2-3y^2)}## for ##z \ge 0##, oriented by the upward unit normal. Evaluate ##\int_{S} \mathit{F} \ dS##. (Hint: Close up this surface and use the Divergence Theorem)

## Homework Equations

## The Attempt at a Solution

It's clear that ##div \ F = 0##, so if I was working with a closed surface, ##\int_{S} \mathit{F} \ dS## would equal 0. For the graph of ##S##, I am unsure as to what "closing up" a surface means. How would one close up a surface?