Let [tex]I[/tex] be the flux of [tex]\mathbf{G}=\left\langle 9 e^y, 3 x^2 e^{x^3}, 0\right\rangle[/tex] through the upper hemisphere [tex]\mathcal{S}[/tex] of the unit sphere.
(a) Find a vector field [tex]\mathbf{A}[/tex] of the form [tex]\langle 0,0, \ldots\rangle[/tex] such that [tex]\mathrm{curl}(\mathbf{A})=\mathbf{G}\space [/tex].
(b) Calculate the circulation of [tex]\mathbf{A}[/tex] around [tex]\partial \mathcal{S}[/tex].
(c) Compute the flux of [tex]\mathbf{G}[/tex] through [tex]\mathcal{S}[/tex]