Let M be the capped cylindrical surface which is the union of two surfaces, a cylinder given by x² + y² = 25, 0 ≤ z ≤ defined by x² + y² + (z − 1)² = 25, z ≥ 1. For the vector field F = (zx + z²y + 5y, z³yx+3x, z¹x²), compute you like. M(V x F). dS = 1, and a hemispherical cap (V x F). dS in any way

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 12E
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Let M be the capped cylindrical surface which is the union of two surfaces, a cylinder given by x² + y² = 25, 0 ≤ z ≤ 1, and a hemispherical cap
defined by x² + y² + (z − 1)² = 25, z ≥ 1. For the vector field F = (zx + z²y + 5y, z³ yx + 3x, zªx²), compute (V x F) · dS in any way
.
you like.
JM (V x F) .dS =
М
Transcribed Image Text:Let M be the capped cylindrical surface which is the union of two surfaces, a cylinder given by x² + y² = 25, 0 ≤ z ≤ 1, and a hemispherical cap defined by x² + y² + (z − 1)² = 25, z ≥ 1. For the vector field F = (zx + z²y + 5y, z³ yx + 3x, zªx²), compute (V x F) · dS in any way . you like. JM (V x F) .dS = М
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