Calculus 3 Quiz
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Let SS be the closed surface consisting of the hemisphere x2+y2+z2=4x^2 + y^2 + z^2 = 4 with z≥0z \geq 0 together with its circular base in the xyxy-plane. Consider the vector field F=⟨x3+yz,y3−xz,z3+xy⟩\mathbf{F} = \langle x^3 + yz, y^3 - xz, z^3 + xy \rangle. If the flux through just the hemispherical portion of SS is 24π24\pi, what is the flux through the circular base?
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