
use Stokes there to eval SSg curl fods F(X,Y,Z) = ett cas(z) ? + V² z...
Use Stokes' Theorem to evaluate curl F. ds. F(x, y, z) = zeli + x cos(y)j + xz sin(y)k, S is the hemisphere x2 + y2 + z2 = 4, y 2 0, oriented in the direction of the positive y-axis.
Use Stokes' Theorem to evaluate S (double integral) curl F · dS. F(x, y, z) = x^2*y^3*z i + sin(xyz) j + xyz k, S is the part of the cone y^2 = x^2 + z^2 that lies between the planes y = 0 and y = 3, oriented in the direction of the positive y-axis.
ie Use Stokes' Theorem to evaluate curl F. ds. F(x, y, z) = x2 sin(z)i + y2 + xyk, S is the part of the paraboloid z = upward. - x2 - y2 that lies above the xy-plane, oriented
4. Use Stokes' Theorem to evaluate F dr. F(x,y,z)-(3z,4x, 2y); C is the circle x2 + y2 4 in the xy-plane with a counterclockwise orientation looking down the positive z-axis. az az F dr-JI, (curl F) n ds and VGy, 1) Hint: use ax' dy
(23 pts) Let F(x, y, z) = ?x + y, x + y, x2 + y2?, S be the top
hemisphere of the unit sphere oriented upward, and C the unit
circle in the xy-plane with positive orientation.
(a) Compute div(F) and curl(F).
(b) Is F conservative? Briefly explain.
(c) Use Stokes’ Theorem to compute ? F · dr by converting it to
a surface integral. (The integral is easy if C
you set it up correctly)
4. (23 pts)...
Use Stokes' Theorem to evaluate sta curl F. ds. F(x, y, z) = xyzi + xyj + x2yzk, S consists of the top and four sides (but not the bottom of the cube with vertices (+3, +3, +3), oriented outward. Need Help? Read It Watch It Talk to a Tutor Submit Answer 33. [-/2.5 Points] DETAILS SCALC8 16.8.018. MY NOTES ASK YOUR Evaluate le (y + 5 sin(x)) dx + (z2 + 3 cos(y)) dy + x3 dz where C...
Evaluate Z Z S curl(F) · dS where F(x, y, z) = (x^ 3 , −z ^3y ^3 , 2x − 4y) and S is the portion of the paraboloid z = x ^2 + y^ 2 − 3 below the plane z = 1 with orientation in the negative z-axis direction.
3. Use Stokes' Theorem to evaluate [ſcurl Ē. d5 where F(x, y, z)= x?y?zi + sin(xyz)ị + xyzk, o is the portion of the cone y² = x² +z? that lies between the planes y=0) and y = 3, oriented in the direction of the positive y-axis. [2187 1/4]
10. Stokes' Theorem and Surface Integrals of Vector Fields a. Stokes' Theorem: F dr- b. Let S be the surface of the paraboloid z 4-x2-y2 and C is the trace of S in the xy-plane. Draw a sketch of curve C in the xy-plane. Let F(x,y,z) = <2z, x, y?». Compute the curl (F) c. d. Find a parametrization of the surface S: G(u,v)- Compute N(u,v) e. Use Stokes' Theorem to computec F dr
10. Stokes' Theorem and Surface Integrals...
use stokes theorem
b. F(x, y, z) =<z?, y, z>, S: 2 = 19x2 - y2, and Cis the trace of S In the xy-plane (positively oriented). Sketch S and C, then Evaluate.