Question

In: Advanced Math

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.

Solutions

Expert Solution

Colby Messinger answered 2 years ago
Next > < Previous

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'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 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.
Evaluate the line integral C F · dr, where C is given by the vector function...
Evaluate the line integral C F · dr, where C is given by the vector function r(t). F(x, y, z) = sin(x) i + cos(y) j + xz k r(t) = t5 i − t4 j + t k, 0 ≤ t ≤ 1
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 Divergence Theorem to evaluate ∫ ∫ S F ⋅ d S where F=〈2x^3,2y^3,4z^3〉 and...
Use the Divergence Theorem to evaluate ∫ ∫ S F ⋅ d S where F=〈2x^3,2y^3,4z^3〉 and  S is the sphere x2+y2+z2=16 oriented by the outward normal.
Use the Divergence Theorem to evaluate ∫∫ ? ∙ ?? where ? = ??2 ?⃑+ (??2...
Use the Divergence Theorem to evaluate ∫∫ ? ∙ ?? where ? = ??2 ?⃑+ (??2 − 3?4 )?⃑+ (?3 + ?2 )? and S is the surface of the sphere of radius 4 with ? ≤ 0 and ? ≤ 0 . would spherical coordinates work?
Use the Stoke’s theorem to evaluate Z Z S (∇×F)·nˆ·dS where F(x, y, z) = (x^2...
Use the Stoke’s theorem to evaluate Z Z S (∇×F)·nˆ·dS where F(x, y, z) = (x^2 z^2,y^2 z^2, xyz) and surface S is part of the paraboloid z = x^2 + y^2 that lies inside the cylinder x^2 + y^2 = 4, oriented upwards. Sketch the surface S and label everything.
verify Stokes' thm.Assume that the surface S is oriented upward F = 2zi - 3xj +...
verify Stokes' thm.Assume that the surface S is oriented upward F = 2zi - 3xj + 4yk ; S that portion of the paraboloid z =16 - x2- y2 for z>=0. My primary is how to convert dS into dA
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT