3. Use Stokes' theorem to evaluate the line integral ?C F·dr = ?S curl F · dS, where F(x, y, z)

Name: 3. Use Stokes' theorem to evaluate the line integral ?C F·dr = ?S curl F · dS, where F(x, y, z) = ?-y², x, z²? and C is the curve of intersection of the plane y + z = 2 and the cylinder x² + y² = 1, oriented counterclockwise when viewed from above. Answer: ?S curl F · dS = ?
Uploaded: 2023-07-04T02:10:05-08:00
Duration: 4 min 41 s
Channel: Adi S
Description: 3. Use Stokes' theorem to evaluate the line integral ?C F·dr = ?S curl F · dS, where F(x, y, z) = ?-y², x, z²? and C is the curve of intersection of the plane y + z = 2 and the cylinder x² + y² = 1, oriented counterclockwise when viewed from above. Answer: ?S curl F · dS = ?

Question

3. Use Stokes&#x27; theorem to evaluate the line integral ?C F·dr = ?S curl F · dS, where F(x, y, z)

Bradley Duda · Accepted Answer

1. First, we need to find the curl of the vector field F. The curl of a vector field is given by

Question

3. Use Stokes' theorem to evaluate the line integral ?_C F·dr = ?_S curl F · dS, where F(x, y, z) = ?-y², x, z²? and C is the curve of intersection of the plane y + z = 2 and the cylinder x² + y² = 1, oriented counterclockwise when viewed from above. Answer: ?_S curl F · dS = ?

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