- 1 (110.38 KiB) Viewed 8 times
a...b...cProblem 4 (13 points) - a) Evaluate and C the boundary of the plane z=1-y. [5 pts.] •F.dr = SS (curl F) on ds F = i 곬 |>²ycos(ky) F. dr where F = z²y cos(xy) i+z²x(1 + cos xy)j + 2zsin(xy) k (2,0,0) 2² 2²x sin xy - 2²y sinay) i (22 cosky - 22yco's ky) j - (2²-2³sin xy² - 2²y sinay) (^ 2 g 7911 = 4√g 19 읇 32 2²x (1+cos Ry) 22 s'^ (^₂) 11.77911 b) Find the outward flux , (F.n)ds of the vector field F = 2xzi + 5y²j – z²k over the region bounded by: z = y, z = 4 - y, z = 2-x², x = 0 and z = 0. [5 pts.] stodes theorem x41 √2 2 4-2 de 5 Sky and diligdy oy - 2 dy da z=y=x -2 2=2-31/1² F(x, y, z) dz dy dx zul-y g x=0 c) Change the order of integration of the following integral to "dydxdz". [3 pts.] =829 √36-92²/23 4-3 y 9 = 1 × ² + 2 == 2 -y z=4-y = 24 y y = 4.