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S is the ellipsoid [tex]x^2+y^2+2z^2=10[/tex]

and

**F**is a vector field [tex]F=(sin(xy),e^x,-yz)[/tex]

Find: [tex]\int \int_S ( \nabla \mbox {x} F) \cdot dS[/tex]

So, I know that Stokes' Theorem states that:

[tex]\int \int_S ( \nabla \mbox {x} F) \cdot dS = \int_{\partial S} F \cdot ds[/tex]

where [tex]\partial S[/tex] equals the boundary of the ellipsoid. How do you find [tex]\partial S[/tex]? My professor just told me that any closed surface has no boundary and therefore the answer is 0, but would someone show me how I can show this? And can someone tell me under what conditions does the answer become 0 using Stokes' Theorem? Thanks a lot.