Question: Use the divergenve theorem to evaluate SF.dS where the vectorfield is given byF(x,y,z)=(z2x,y33+cos(z),x2z+y2) and Sis the top hald of the sphere x2+y2+z2=1. Note that Sis

Use the divergenve theorem to evaluate SF.dS where the vectorfield is given byF(x,y,z)=(z2x,y33+cos(z),x2z+y2) and Sis the top hald of the sphere x2+y2+z2=1. Note that Sis not a closed surface. First compute integrals aver S1and S2, where S1is the disk x2+y21, oriented downward and S2=S2S.

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