Use Stokes' theorem to change ∫∫?∇?⋅?∫∫S∇F⋅NdS to an equivalent surface integral and evaluate it, where?=x?+y2?+xyz? F=xi+y2j+xyzk,? N is the upward unit normal, and? S is the part of the paraboloid z=4-x2-y2z=4-x2-y2 with z≥0z≥0.

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Use Stokes' theorem to change ∫∫?∇*?⋅?∫∫S∇*F⋅NdS to an equivalent surface integral and evaluate it, where?=x?+y2?+xyz? F=xi+y2j+xyzk,? N is the upward unit normal, and? S is the part of the paraboloid z=4-x2-y2z=4-x2-y2 with z≥0z≥0.

Use Stokes' theorem to change ∫∫?∇?⋅?∫∫S∇F⋅NdS to an equivalent surface integral and evaluate it, where?=x?+y2?+xyz? F=xi+y2j+xyzk,? N is the upward unit normal, and? S is the part of the paraboloid z=4-x2-y2z=4-x2-y2 with z≥0z≥0.