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Evaluate SFdS\iint _ { S } \mathbf { F } \cdot d \mathbf { S }

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Evaluate SFdS\iint _ { S } \mathbf { F } \cdot d \mathbf { S } , that is, find the flux of F\mathbf { F } across SS .
F(x,y,z)=4zi+yj3xk;S\mathbf { F } ( x , y , z ) = - 4 z \mathbf { i } + y \mathbf { j } - 3 x \mathbf { k } ; \mathrm { S } is the hemisphere z=4x2y2;nz = \sqrt { 4 - x ^ { 2 } - y ^ { 2 } } ; \mathbf { n } points upward

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