- F Dr Ss Curl F On Ds Problem 4 13 Points S S Curl Finds A Evaluate F Dr Where F Z Y Cos Xy I Z X 1 Cos X 1 (114 KiB) Viewed 11 times
"F.dr = SS (curl F) on ds. Problem 4 (13 points) S'S curl Finds a) Evaluate F. dr where F = z²y cos(xy)i + z²x(1 + cos xy)j + 2zsin(xy) k and C the boundary of the plane z=1-y. [5 pts.] 19 32 FA by | (2,0,0) (2²y cos(Ay) 2²x (1+cos Ry) 2 z s'n (^y) 2² 2² x sin ky -2²y sinay) i = (22 cosay - 22yco's Ay) J (2²-2³sin kys - 2²y sinay) ( 2 g уди * Jg b) Find the outward flux ff (F.n)ds of the vector field F = 2xzi + 5y²j-z²k over the region bounded by: z = y, z = 4-y, z = 2 - 2x², x = 0 and z = 0. [5 stockes theorem pts.] 9 = 1/2 x ² 11.7g|| على 12 x+1 2 24-2 [Sky O digdy oy - 2 dy da z=y+ S²₁ zul-y F(x, y, z) dz dy dx x=0 c) Change the order of integration of the following integral to "dydxdz". [3 pts.] V/36-92²/23 =32y ***I f z=4-y