Note:- you can choose any right handed rectangular co- ordinate system.
Use Stokes' Theorem to evaluate sta curl F. ds. F(x, y, z) = xyzi + xyj...
Help Entering Answers (1 point) Use Stokes' Theorem to evaluate ll curl F. dS where F(x, y, z) = xyzi + 3xyj + 2x2yzk and S consists of the top and the four sides (but not the bottom) of the cube with vertices (+2, +2, +2), oriented outward. Since the box is oriented outwards the boundary curve must be transversed when viewed from the top. A parametrization for the boundary curve C seen below from above can be given by:...
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.
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
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.
Let F = < x-eyz, xexx, z?exy >. Use Stokes' Theorem to evaluate slice curlĒ ds, where S is the hemisphere x2 + y2 + z2 = 1, 2 > 0, oriented upwards.
Please show work Page 1 10. Use Stokes Theorem to evaluate S. curl F. ds F = (x, y, z) = z² i + 2xj + y2k, S:z = 1 - x2 - y2, z 20
6. -1.25 points My Notes Evaluate (y 3 sin x) dx + (z2 +7 cos y) dy x3 dz COS JC where C is the curve r(t) - (sin t, cos t, sin 2t), 0 s t s 27. (Hint: Observe that C lies on the surface z - 2xy.) F dr- 6. -1.25 points My Notes Evaluate (y 3 sin x) dx + (z2 +7 cos y) dy x3 dz COS JC where C is the curve r(t) -...
Verify that Stokes' Theorem is true for the vector field Help Entering Answers (1 point) Verify that Stokes' Theorem is true for the vector field F -yi+ zj + xkand the surface S the hemisphere x2 + y2 + z2-25, y > 0oriented in the direction of the positive y- axis To verify Stokes' Theorem we will compute the expression on each side. First compute curl F dS curl F The surface S can be parametrized by S(s, t) -...
Use Stokes' Theorem to evaluate les F. dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = (x + y2)i + (y + z2)j + (z + x2)k, C is the triangle with vertices (3, 0, 0), (0, 3,0), and (0, 0, 3). Need Help? Read it Watch It Master It Talk to a Tutor
Use Stokes' Theorem (in reverse) to evaluate Sf (curl F). n ds where F = 5yzi + 9x j +2yze+'k ,S is the portion of the paraboloid z = x2 + aby2 for 0 sz s 3, and the unit normal on S points away from the z-axis. 16 Enter your answer symbolically, as in these examples