Consider the following cube in R³: V = {(x, y, z) € R³:0≤x≤ 1,0 ≤ y ≤ 1,0 ≤ ≤ 1}. Let S denote the boundary of the cube and let F(x, y, z) be the vector field given by F(x, y, z) = (x² sin(ny)ze², z, xy²). Compute the surface integral of the second kind (flux integral) JS.F. where n denotes the normal vector to S pointing outwards of V. Fn dS: •//.F. S - F. dS,

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Consider the following cube in R³:
V = {(x, y, z) € R³ : 0 ≤ x ≤ 1,0 ≤ y ≤ 1,0 ≤ z ≤ 1}.
Let S denote the boundary of the cube and let F(x, y, z) be the vector field given
by
F(x, y, 2)
(x² sin(ny)ze², z, xy²).
Compute the surface integral of the second kind (flux integral)
1's
=
Fn dS
= [[₁₂₁
=
F. ds.
9
where n denotes the normal vector to S pointing outwards of V.
Transcribed Image Text:Consider the following cube in R³: V = {(x, y, z) € R³ : 0 ≤ x ≤ 1,0 ≤ y ≤ 1,0 ≤ z ≤ 1}. Let S denote the boundary of the cube and let F(x, y, z) be the vector field given by F(x, y, 2) (x² sin(ny)ze², z, xy²). Compute the surface integral of the second kind (flux integral) 1's = Fn dS = [[₁₂₁ = F. ds. 9 where n denotes the normal vector to S pointing outwards of V.
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