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ok no idea what to do with this z in the this problem, cause im teaching this to myself i don't know what to do and im asking for some help thanks anyone...

ok well im trying to compute this problems with Stroke's therom

the surface is [tex] z = \sqrt{4-x^2-y^2} [/tex] above the xy-plane

and [tex] \vec{F} = <2x-y,yz^2,y^2z>[/tex]

ok using stoke's i do [tex]\nabla X \vec{F} = \vec{k}[/tex]

and...

then instead of finding the normal vector with the surface z, i did, [tex]f(x,y,z) = 4-x^2-y^2-z^2[/tex] which [tex]\vec{n} = \nabla f = <-2x,-2y,-2z>[/tex] but we want a normal vector pointing out from the surface, so..(also note i didn't but the normalizing sqrt cause it comes out in the dS -> dA change) [tex] -\vec{n} = <2x,2y,2z>[/tex] and then fallowing stoke's...[tex]\vec{k} \bullet\vec{n} = 2z -> \int\int_{A}2zdydx[/tex] but my understanding of a surface intergral is that z is 0 so that the surface is actually an area projected on to the xy-plane, what am to do in these situations? or did i just do it wrong?

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# What do i do with z?

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