12. 13. 14. 15. 16. Is the following vector eld conservative. If yes, nd a potential function for it: F = (2:1: sin(2y) 392.. 2 633; + 232 cos(2y)). Given the f' in the previous problem, evaluate / F1 - (E where C is the eastern semicircle of radius 2 C centered at the origin oriented clockwise. Evaluate ff de where S is given by the region 51:2 + y2 + 2:2 = 4, 0 g y g 2. .5 Evaluate // 3:2 d3 where S is the sphere of radius 1 contained in the rst octant. .5 Given Ii" 2 (82,2,17), and G(r,s) = (7-3,?- + 3,1") from 0 g 'r g 1 and 0 g s g 1, find ff Ii"- rig 3 oriented by T, x 1