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 - z,yz,-xz), S consists of the five faces of the cube 0 s x, y,z s 2, unit normal n is outward Answer: -4 (b) F(x, y,z) bounded by the three coordinate planes and the plane 3x + y + 3z = 6. The unit normal n is outward of the tetrahedron (xz,-y, x2y) S consists of three faces not in the xz-plane 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 - z,yz,-xz), S consists of the five faces of the cube 0 s x, y,z s 2, unit normal
n is outward
Answer: -4
(b) F(x, y,z)
bounded by the three coordinate planes and the plane 3x + y + 3z = 6. The unit normal n is
outward of the tetrahedron
(xz,-y, x2y) S consists of three faces not in the xz-plane of the tetrahedron
=
Answer: 4/3.
Transcribed Image Text: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 - z,yz,-xz), S consists of the five faces of the cube 0 s x, y,z s 2, unit normal n is outward Answer: -4 (b) F(x, y,z) bounded by the three coordinate planes and the plane 3x + y + 3z = 6. The unit normal n is outward of the tetrahedron (xz,-y, x2y) S consists of three faces not in the xz-plane of the tetrahedron = Answer: 4/3.
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