Let the surface S₁ be the upper hemisphere x² + y² + z² = 1, with z ≥ 0 = Let the surface S₂ be the upper cylinder x² + y² 1, with 0≤ z ≤ 1, with the top closed off (so at z = 1, the top of the surface is a disk, thus atz = 1 we have x² + y² ≤ 1), but the bottom of the surface is open. Let F be the vector field (xy, yz, xz + xyz) Let be the normal oriented to point away from the origin. Compute S [V x F].. .ndS₁ - [V x F] S₂ .nds 2
Let the surface S₁ be the upper hemisphere x² + y² + z² = 1, with z ≥ 0 = Let the surface S₂ be the upper cylinder x² + y² 1, with 0≤ z ≤ 1, with the top closed off (so at z = 1, the top of the surface is a disk, thus atz = 1 we have x² + y² ≤ 1), but the bottom of the surface is open. Let F be the vector field (xy, yz, xz + xyz) Let be the normal oriented to point away from the origin. Compute S [V x F].. .ndS₁ - [V x F] S₂ .nds 2
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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![Let the surface S₁ be the upper hemisphere x² + y² + z² = 1, with z ≥ 0
Let the surface S₂ be the upper cylinder x² + y²
2
top closed off (so at z
x² + y² ≤ 1), but the bottom of the surface is open.
1, with 0≤ z ≤ 1, with the
1, the top of the surface is a disk, thus atz 1 we have
=
Let F be the vector field (xy, yz, xz + xyz)
Let be the normal oriented to point away from the origin.
Compute
16.10
S₁
[VxF].n S₁ 1
- √ [V x F] . n d ₂
2
S₂](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1d5e88e6-b1af-4aea-9b08-2dadd85f5e2c%2Fc935d9da-642e-40ab-9f89-16beee9d8203%2Fk562dsi_processed.png&w=3840&q=75)
Transcribed Image Text:Let the surface S₁ be the upper hemisphere x² + y² + z² = 1, with z ≥ 0
Let the surface S₂ be the upper cylinder x² + y²
2
top closed off (so at z
x² + y² ≤ 1), but the bottom of the surface is open.
1, with 0≤ z ≤ 1, with the
1, the top of the surface is a disk, thus atz 1 we have
=
Let F be the vector field (xy, yz, xz + xyz)
Let be the normal oriented to point away from the origin.
Compute
16.10
S₁
[VxF].n S₁ 1
- √ [V x F] . n d ₂
2
S₂
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