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Given a vector overline rm u = frac 1 3 left(...

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Calculus
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Given a vector \[\overline {\rm{u}} = \frac{1}{3}\left( { - {{\rm{y}}^3}{\rm{\hat i}} + {{\rm{x}}^3}{\rm{\hat j}} + {{\rm{z}}^3}{\rm{\hat k}}} \right)\]     and \[{{\rm{\hat n}}}\] as the unit normal vector to the surface of the hemisphere (x2 + y2 + z2 = 1; z ≥ 0), the value of integral \[\int {\left( {\nabla \times \overline {\rm{u}} } \right) \cdot {\rm{\hat n}}} {\rm{dS}}\]    evaluated on the curved surface of the hemisphere S is

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Correct Answer: Option B
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