Divergence theorem Consider the vector field F(x, y, z) = y¹zi+xz³j+x²zk and the surface S that is the boundary of the outward oriented rectangular prism defined by 0 ≤ x ≤ 5 -8 ≤ y ≤ −5 -5 ≤ z≤1 Tasks (a) Let S₁ denote the part of the surface S where x = 5, evaluate IJs FdS (b) Let S₂ denote the part of the surface S where y = -8, evaluate J Fas JJ Fas S3 (c) Let S3 denote the part of the surface S where z = 1, evaluate (d) divF = -71143.2 = (e) Evaluate JIS = -1956.25 Fas=
Divergence theorem Consider the vector field F(x, y, z) = y¹zi+xz³j+x²zk and the surface S that is the boundary of the outward oriented rectangular prism defined by 0 ≤ x ≤ 5 -8 ≤ y ≤ −5 -5 ≤ z≤1 Tasks (a) Let S₁ denote the part of the surface S where x = 5, evaluate IJs FdS (b) Let S₂ denote the part of the surface S where y = -8, evaluate J Fas JJ Fas S3 (c) Let S3 denote the part of the surface S where z = 1, evaluate (d) divF = -71143.2 = (e) Evaluate JIS = -1956.25 Fas=
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:Divergence theorem
Consider the vector field
F(x, y, z) = y¹zi+xz³j+x²zk
and the surface S that is the boundary of the outward oriented
rectangular prism defined by
0 ≤ x ≤ 5
-8 ≤ y ≤ −5
-5 ≤ z≤1
Tasks
(a) Let S₁ denote the part of the surface S where x = 5,
evaluate
IJs
FdS
(b) Let S₂ denote the part of the surface S where y = -8,
evaluate
JJ Fas
JJ Fas
S3
(c) Let S3 denote the part of the surface S where z = 1,
evaluate
(d)
divF
= -71143.2
=
(e) Evaluate
JIS
=
-1956.25
Fas=
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