Question
Asked Nov 29, 2019
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65. Transform the surface integral curl(F dS into a line integral using Stokes' theorem, and
evaluate the line integral:
(a) F(x, y, z(y-, yz,-xz), S consists of the five faces of the cube 0
n is outward
2, unit normal
x, y, z
Answer: -4
(b) F(x, y, z) (xz,-y,x2y), S consists of three faces not in the xz-plane of the tetrahedron
bounded by the three coordinate planes and the plane 3.x + y + 3z = 6. The unit normal n is
outward of the tetrahedron.
Answer: 4/3
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65. Transform the surface integral curl(F dS into a line integral using Stokes' theorem, and evaluate the line integral: (a) F(x, y, z(y-, yz,-xz), S consists of the five faces of the cube 0 n is outward 2, unit normal x, y, z Answer: -4 (b) F(x, y, z) (xz,-y,x2y), S consists of three faces not in the xz-plane of the tetrahedron bounded by the three coordinate planes and the plane 3.x + y + 3z = 6. The unit normal n is outward of the tetrahedron. Answer: 4/3

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Step 1

 

We’ll answer the first question since the exact one wasn’t specified. Please submit a new question specifying the one you’d like answered.

Stokes theorem – If S be a smooth surface which is bounded by a simple, closed and smooth boundary curve, then

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C

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Step 2

(a)Consider the given function and the surface as,

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F yz,yzxz) and surface is 0sx,y,z<2

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Step 3

Applying stokes theorem on t...

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F=y-z,yz,-z) and dr = (dk,dy,dz) then F.dr ((y-z)dr, yzcy, xzdz) Then by Stokes theorem CrIdsFdr=fl(y-z)dk+yzdy -xzdz) C

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