Let M be the capped cylindrical surface which is the union of two surfaces, a cylinder given by x² + y² = 9, 0 ≤ z < 1, and a hemispherical cap defined by x² + y² + (z − 1)² = 9, z ≥ 1. For the vector field F = (x²), : (zx + z²y +2y, z³yx + 4x, z²x² compute M (V × F) · dS in any way you like. ſſ₁(▼ × F) · dS = •
Let M be the capped cylindrical surface which is the union of two surfaces, a cylinder given by x² + y² = 9, 0 ≤ z < 1, and a hemispherical cap defined by x² + y² + (z − 1)² = 9, z ≥ 1. For the vector field F = (x²), : (zx + z²y +2y, z³yx + 4x, z²x² compute M (V × F) · dS in any way you like. ſſ₁(▼ × F) · dS = •
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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Transcribed Image Text:Let M be the capped cylindrical surface
which is the union of two surfaces, a cylinder
given by x² + y² = 9, 0 ≤ z < 1, and a
hemispherical cap defined by
x² + y² + (z − 1)² = 9, z ≥ 1. For the
vector field
F
=
(x²),
: (zx + z²y +2y, z³yx + 4x, z²x²
compute M (V × F) · dS in any way you
like.
ſſ₁(▼ × F) · dS
=
•
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