Question

In: Math

Use Stokes' theorem to compute the circulation F · dr where F = 8xyz, 2y2z, 5yz...

Use Stokes' theorem to compute the circulation

F · dr

where F =

8xyz, 2y2z, 5yz

and C is the boundary of the portion of the plane

2x + 3y + z = 6

in the first octant. Here C is positively oriented with respect to the plane whose orientation is upward.

Solutions

Expert Solution


Related Solutions

Use Stokes' Theorem to evaluate C F · dr where C is oriented counterclockwise as viewed...
Use Stokes' Theorem to evaluate C 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 (7, 0, 0), (0, 7, 0), and (0, 0, 7).
Use Stokes' Theorem to evaluate C F · dr where C is oriented counterclockwise as viewed...
Use Stokes' Theorem to evaluate C F · dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = xyi + 3zj + 7yk, C is the curve of intersection of the plane x + z = 10 and the cylinder x2 + y2 = 9.
Use Stokes' Theorem to evaluate C F · dr where C is oriented counterclockwise as viewed...
Use Stokes' Theorem to evaluate C F · dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = xyi + 3zj + 5yk, C is the curve of intersection of the plane x + z = 2 and the cylinder x^2 + y^2 = 144.
Use Stokes' Theorem to find the circulation of F⃗ =2yi⃗ +2zj⃗ +4xk⃗  around the triangle obtained by...
Use Stokes' Theorem to find the circulation of F⃗ =2yi⃗ +2zj⃗ +4xk⃗  around the triangle obtained by tracing out the path (3,0,0) to (3,0,4), to (3,4,4) back to (3,0,0). Circulation = ∫CF⃗ ⋅dr⃗  = Second time I've asked this question because chegg cant solve this problem correct. 24sqrt(2) is the wrong answer
(1 point) Let F=−3yi+4xjF=−3yi+4xj. Use the tangential vector form of Green's Theorem to compute the circulation...
(1 point) Let F=−3yi+4xjF=−3yi+4xj. Use the tangential vector form of Green's Theorem to compute the circulation integral ∫CF⋅dr∫CF⋅dr where C is the positively oriented circle x2+y2=25x2+y2=25.
Use Stokes's Theorem to evaluate F · dr C . C is oriented counterclockwise as viewed...
Use Stokes's Theorem to evaluate F · dr C . C is oriented counterclockwise as viewed from above. F(x,y,z) = 6xzi + yj + 6xyk S: z = 16 - x^2 - y^2, z ≥ 0
Use the Divergence Theorem to evaluate S F · dS, where F(x, y, z) = z2xi...
Use the Divergence Theorem to evaluate S F · dS, where F(x, y, z) = z2xi + y3 3 + cos z j + (x2z + y2)k and S is the top half of the sphere x2 + y2 + z2 = 4. (Hint: Note that S is not a closed surface. First compute integrals over S1 and S2, where S1 is the disk x2 + y2 ≤ 4, oriented downward, and S2 = S1 ∪ S.)
Use the extended divergence theorem to compute the total flux of the vector field F(x, y,...
Use the extended divergence theorem to compute the total flux of the vector field F(x, y, z) = −3x2 + 3xz − y, 2y3 − 6y, 9x2 + 4z2 − 3x outward from the region F that lies inside the sphere x2 + y2 + z2 = 25 and outside the solid cylinder x2 + y2 = 4 with top at z = 1 and bottom at z = −1.
proof of the general stokes theorem using the greens and divergence theorem that is understandable by...
proof of the general stokes theorem using the greens and divergence theorem that is understandable by a calculus student
Write down Green’s Circulation Theorem. Explain when Green’s Circulation Theorem applies and when it does not....
Write down Green’s Circulation Theorem. Explain when Green’s Circulation Theorem applies and when it does not. Give an example of Green’s Circulation Theorem showing the function, the integral and drawing the region.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT