Compute the flux of the vector field ( vec{F} = z vec{i} + 2x vec{j} ) through the parameterized surface S oriented upward and given, for ( 0 le s le 1, quad 2 le t le 4 ), by ( x = s^2, quad y = 2s + t^2, quad z = 6t. ) flux = -408
Added by John C.
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First, we need to find the normal vector to the surface S. We can do this by taking the cross product of the partial derivatives of the parameterization: r_s = <1, 2, 0> r_t = <0, 6, 0> n = r_s x r_t = <-12, 0, 2> Note that we chose the order of the cross Show more…
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Compute the flux of the vector field F = zi + 2xj through the parameterized surface S oriented upward and given, for 0 ≤ s ≤ 1, 2 ≤ t ≤ 4, by x = s², y = 2s + t², z = 6t.
Madhur L.
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