Question

Use Stokes' Theorem to evaluate ∫ C F · dr where F = (x + 5z) i + (3x + y) j + (4y − z) k and C is the curve of intersection of the plane x + 2y + z = 16 with the coordinate planes

Answer #1

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Use Stokes' Theorem to evaluate
∫
C
F · dr
where F = (x +
8z) i + (6x +
y) j + (7y −
z) k and C is the curve of
intersection of the plane x + 3y + z
= 24 with the coordinate planes.
(Assume that C is oriented counterclockwise as viewed from
above.) Please explain steps. Thank you:)

Use Stokes' Theorem to evaluate
C
F · dr
where C is oriented counterclockwise as viewed from
above.
F(x, y, z) = 5yi + xzj + (x + y)k,
C is the curve of intersection of the plane
z = y + 7
and the cylinder
x2 + y2 = 1.

Use Stokes' Theorem to evaluate ∫ C F ⋅ dr. In each case C is
oriented counterclockwise as viewed from above. F ( x , y , z ) = e
− x ˆ i + e x ˆ j + e z ˆ k
C is the boundary of the part of the plane 2 x + y + 2 z = 2 in
the first octant ∫ C F ⋅ d r =

Use Stokes" Theorem to evaluate (F-dr where F(x, y, z)=(-y , x-z
, 0) and the surface S is the part of the paraboloid : z = 4- x^2 -
y^2 that lies above the xy-plane. Assume C is oriented
counterclockwise when viewed from above.

Use Stokes' Theorem to evaluate
C
F · dr
where C is oriented counterclockwise as viewed from
above.
F(x, y,
z) = yzi +
6xzj +
exyk,
C is the circle
x2 +
y2 = 9, z = 2.

Use Divergence theorem to evaluate surface integral S F ·n dA
where S is the surface of the solid enclosed by the tetrahedron
formed by the coordinate planes x = 0, y = 0 and z = 0 and the
plane 2x + 2y + z = 6 and F = 2x i − x^2 j + (z − 2x + 2y) k.

Use Stokes' Theorem to evaluate the integral
∮CF⋅dr=∮C8z^2dx+8xdy+2y^3dz where C is the circle x^2+y^2=9 in the
plane z=0 .

Evaluate∫ C F ⋅ d r , where F(x,y,z)={e^−4x,e^2x,1e^z} and C is
the boundary of the part of the plane 3x+7y+5z=3 lying in the first
octant, traversed counterclockwise as viewed from above. HINT: Use
Stokes' Theorem.

Use the Divergence Theorem to evaluate
F.N dS
and find the outward flux of F through the surface of the
solid bounded by the graphs of the equations.
F(x, y, z) = xi + xyj + zk
Q: solid region bounded by the coordinate planes and the plane
3x + 4y + z = 24

Use the Divergence Theorem to evaluate
S
F · N dS
and find the outward flux of F through the
surface of the solid bounded by the graphs of the equations.
F(x, y,
z) =
x2i +
xyj +
zk
Q: solid region bounded by the coordinate
planes and the plane 3x + 4y +
6z = 24

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