Use the surface integral in Stokes' Theorem to calculate the circulation of the field F around the curve C in the indicated direction. F=yi+xzj+x²k C: The boundary of the triangle cut from the plane 2x+y+z=2 by the first octant, counterclockwise when viewed from above. The circulation is (Tuno on fraction
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- Use Green's Theorem to calculate the circulation of F = 2y i + 8xy j around the unit circle, oriented counterclockwise. circulation =Use Green's Theorem to calculate the circulation of F = 2y i + 8xy j around the unit circle, oriented counterclockwise. circulation = -piUse Stokes' Theorem to calculate the circulation of the field F around the curve C in the indicated direction 3₁ F = 2yi +5xj + z³k; C: the counterclockwise path around the perimeter of the triangle in the x-y plane formed from the x-axis, y- axis, and the line y = 5 - 6x
- Use Green's Theorem to calculate the circulation of F =2yi +xyj around the unit circle, oriented counterclockwise.Use the surface integral in Stokes' Theorem to calculate the circulation of the field F around the curve C in the indicated direction. F = yi+xzj+x²k C: The boundary of the triangle cut from the plane 10x + y + z = 10 by the first octant, counterclockwise when viewed from above. The circulation is (Type an integer or a fraction.)Evaluate the circulation of G = xyi + zj + 4yk around a square of side 4, centered at the origin, lying in the yz-plane, and oriented counterclockwise when viewed from the positive x-axis. Circulation = Jo F. dr =
- use the surface integral in Stokes’ Theorem to calculate the circulation of the field F around the curve C in the indicated direction. F = yi + xzj + x2k C: The boundary of the triangle cut from the plane x + y + z = 1 by the first octant, counterclockwise when viewed from above.Let F=(9xy,7y,8z)=(9xy,7y,8z).The curl of F=(Is there a function f such that F=∇f=∇? (y/n)Use Stokes' Theorem to find the circulation of the vector field F = 2xzi + (3x + yz)j + x²k around the paths. C, is the circle x? + y = 4, z = 5, oriented counterclockwise when viewed from above. circulation =
- Use the surface integral in Stokes' Theorem to calculate the circulation of the field F around the curve C in the indicated direction. F= yi+ xzj +x*k C: The boundary of the triangle cut from the plane 3x+ y +z = 3 by the first octant, counterclockwise when viewed from above. The circulation is (Type an integer or a fraction.)= Use Stokes' Theorem to find the circulation of F 5y + 5zj+2ak around the triangle obtained by tracing out the path (6,0,0) to (6,0, 6), to (6, 3, 6) back to (6,0,0). Circulation = - dr = -45