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
Colby Messinger answered 2 years agoRelated 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
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