15_6_12 - 12. : r = eu cos vi + eu sin vj + uk, (0 u 1, 0 v...

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12. : r = e u cos v i + e u sin v j + u k , ( 0 u 1 , 0 v π) , has upward surface element ˆ N dS = r u × r ∂v du d v = ( - e u cos v i - e u sin v j + e 2 u k ) du d v. The flux of F = yz i - xz j + ( x 2 + y 2 ) k upward through is ZZ F ˆ N dS = Z 1 0 du Z π 0 ( - ue 2 u
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