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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.

User Ed Mazur
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User OoMaR JOhUr
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