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5. (a) Use Stokes' theorem to calculate the circulation of the vector field F around the curve C. That is, find fF-dr when F = (y² + z²)i + (x² + z²)j + (x² + y²) k and C is the boundary of the triangle cut from the plane x+y+z = 1 by the first octant. The curve C is oriented counterclockwise when viewed from above. (b) Use Stokes' Theorem to calculate × FdS when F = (3y, 5 – 2x, z² – 2). S is parameterized by r(r, 0) = (r cos 0,r sin 0,5-r) with 0≤r≤5,0 ≤0 ≤ 2 and is oriented upwards. S

5. (a) Use Stokes' theorem to calculate the circulation of the vector field F around the curve C. That is, find fF-dr when F = (y² + z²)i + (x² + z²)j + (x² + y²) k and C is the boundary of the triangle cut from the plane x+y+z = 1 by the first octant. The curve C is oriented counterclockwise when viewed from above. (b) Use Stokes' Theorem to calculate × FdS when F = (3y, 5 – 2x, z² – 2). S is parameterized by r(r, 0) = (r cos 0,r sin 0,5-r) with 0≤r≤5,0 ≤0 ≤ 2 and is oriented upwards. S

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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5. (a) Use Stokes' theorem to calculate the circulation of the vector field F around the curve C. That is, find fF-dr when F = (y² + z²)i + (x² + z²)j + (x² + y²) k and C is the boundary of the triangle cut from the plane x+y+z = 1 by the first octant. The curve C is oriented counterclockwise when viewed from above. (b) Use Stokes' Theorem to calculate × FdS when F = (3y, 5 – 2x, z² – 2). S is parameterized by r(r, 0) = (r cos 0,r sin 0,5-r) with 0≤r≤5,0 ≤0 ≤ 2 and is oriented upwards. S
Transcribed Image Text:5. (a) Use Stokes' theorem to calculate the circulation of the vector field F around the curve C. That is, find fF-dr when F = (y² + z²)i + (x² + z²)j + (x² + y²) k and C is the boundary of the triangle cut from the plane x+y+z = 1 by the first octant. The curve C is oriented counterclockwise when viewed from above. (b) Use Stokes' Theorem to calculate × FdS when F = (3y, 5 – 2x, z² – 2). S is parameterized by r(r, 0) = (r cos 0,r sin 0,5-r) with 0≤r≤5,0 ≤0 ≤ 2 and is oriented upwards. S
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