15_6_10 - 10. : r = u 2 vi + uv 2 j + v 3 k, (0 u 1, 0 v...

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10. : r = u 2 v i + u v 2 j + v 3 k , ( 0 u 1 , 0 v 1 ) , has upward surface element ˆ N dS = r u × r ∂v du d v = ( 2 u v i + v 2 j ) × ( u 2 i + 2 u v j + 3 v 2 k ) du d v = ( 3 v 4 i - 6 u v 3 j + 3 u 2 v 2 k ) du d v. The flux of F = 2 x i + y j + z k upward through is ZZ F ˆ N dS
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