1. Let V be the region between the two spheres r2 + y2 + x2 = 1 and 22 + y2 + x2 = 2 for z > 0. Let S be the closed surf

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1 Let V Be The Region Between The Two Spheres R2 Y2 X2 1 And 22 Y2 X2 2 For Z 0 Let S Be The Closed Surf 1 (197.69 KiB) Viewed 25 times

1. Let V be the region between the two spheres r2 + y2 + x2 = 1 and 22 + y2 + x2 = 2 for z > 0. Let S be the closed surface surrounding V. S consists of three surfaces, S1, S2 and B, shown below. - B Let F = (0, 0, 222). Calculate the surface integral SSsFoñds by adding up the surface integrals over Si, S2 and B. 2. Let F and S be defined exactly as in problem 1. Calculate SS, Fonds by using the Divergence Theorem. 3. Let F = (2x2 +z, 0, r2 + ). Is F a conservative vector field? If it is, find a scalar valued function o so that F = V0. If F is not a conservative vector field, prove it.