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Multivariable & Vectorhard
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Consider the vector field F⃗=⟨xy,yz,zx⟩\vec{F} = \langle xy, yz, zx \rangleF=⟨xy,yz,zx⟩. Calculate the flux of ∇×F⃗\nabla \times \vec{F}∇×F across the surface SSS defined by x2+y2+z2=1,z≥0x^2 + y^2 + z^2 = 1, z \geq 0x2+y2+z2=1,z≥0, with upward orientation.