Question

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 .

Answer #1

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

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 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) = 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
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:)

(1 point)
Evaluate the line integral ∫CF⋅dr∫CF⋅dr, where F(x,y,z)=3xi+4yj-zk
and C is given by the vector function r(t)=〈sint,cost,t〉,
0≤t≤3π/2.

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 Green’s theorem to evaluate the integral: ∫(-x^2y)dx
+(xy^2)dy where C is the boundary of the region enclosed by y=
sqrt(9 − x^2) and the x-axis, traversed in the counterclockwise
direction.

Use Stokes' Theorem to
evaluate the surface integral
∬ G curl F ⋅ n d S
where F ( x , y , z )
= ( z 2 − y ) i + ( x + y z ) j + x z k , G is the surface
G = { ( x , y , z ) |
z = 1 − x 2 − y 2 , z ≥ 0 }
and n
is the upward...

Evaluate the line integral ∫CF⋅dr, where F(x,y,z)=5xi+yj−2zk and
C is given by the vector function r(t)=〈sint,cost,t〉, 0≤t≤3π/2.

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