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Evaluate ∬SF⋅dS\iint _ { S } \mathbf { F } \cdot d \mathbf { S }

Question 118

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Evaluate ∬SF⋅dS\iint _ { S } \mathbf { F } \cdot d \mathbf { S } , that is, find the flux of F across S. F(x,y,z)=4xi+2yj+4k\mathbf { F } ( x , y , z ) = 4 x \mathbf { i } + 2 y \mathbf { j } + 4 \mathbf { k } ; S is the part of the paraboloid z=x2+y2z = x ^ { 2 } + y ^ { 2 } between the planes z = 0 and z = 5; n points upward.

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