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Find the Flux of the Vector Field F Across the Surface

question 271

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Find the flux of the vector field F across the surface S in the indicated direction.
- F(x,y,z) =7xi+7yj+2k,S\mathbf { F } ( \mathrm { x } , \mathrm { y } , \mathrm { z } ) = 7 \mathrm { x } \mathbf { i } + 7 \mathrm { yj } + 2 \mathbf { k } , \mathrm { S } is the surface cut from the bottom of the paraboloid z=x2+y2\mathrm { z } = \mathrm { x } ^ { 2 } + \mathrm { y } ^ { 2 } by the plane z=2z = 2 , direction is outward

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