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Consider the cone Si given by z = vx2 + y? where (x, y) E D the disk of radius 2, with upwards orientation. We close it with its "lid" S2, the horizontal disk of radius 2 at level 2, with upwards orientation. We also consider the vector field F(x, y, z) = (x, y, 1). 1. Compute the flux through the cone F . as. 2. Compute the flux through the lid JJS2 F . as. 3. Deduce the flux through the surface S consisting of the cone with its lid, with outwards orientation. Careful of signs! 4. Recover the result of Question 3 using the divergence theorem