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Compute the following: (a) Integrate the following vector field F = 2x cos(2)i + 2y cos(z)j — (x² + y²) sin(2)k over the boundary of the hypocycloid shown below: Hypocycloid: 2²/3 + y2/3 = ²/3 x = a cos³ (0) y = a sin³ (0) (b) Consider the following vector field F = r³yỉ+ y sin(2)j — ryz³k. Compute V = V ×F, and integrate the outward flux of the new vector field V through the spherical surface as defined by x² + y² + 2² = 1.

Compute the following: (a) Integrate the following vector field F = 2x cos(2)i + 2y cos(z)j — (x² + y²) sin(2)k over the boundary of the hypocycloid shown below: Hypocycloid: 2²/3 + y2/3 = ²/3 x = a cos³ (0) y = a sin³ (0) (b) Consider the following vector field F = r³yỉ+ y sin(2)j — ryz³k. Compute V = V ×F, and integrate the outward flux of the new vector field V through the spherical surface as defined by x² + y² + 2² = 1.

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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Compute the following: (a) Integrate the following vector field F = 2r cos(z)i + 2y cos(z)j − (r² + y²) sin(z)k over the boundary of the hypocycloid shown below: Hypocycloid: = x2/3 + y2/3 - ²/3 x = a cos³ (0) y = a sin³ (0) (b) Consider the following vector field F = x³yi+y sin(2)j-ryz³k. Compute V = V XF, and integrate the outward flux of the new vector field V through the spherical surface as defined by x² + y² + x² = 1.
Transcribed Image Text:Compute the following: (a) Integrate the following vector field F = 2r cos(z)i + 2y cos(z)j − (r² + y²) sin(z)k over the boundary of the hypocycloid shown below: Hypocycloid: = x2/3 + y2/3 - ²/3 x = a cos³ (0) y = a sin³ (0) (b) Consider the following vector field F = x³yi+y sin(2)j-ryz³k. Compute V = V XF, and integrate the outward flux of the new vector field V through the spherical surface as defined by x² + y² + x² = 1.
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