F(x, y, z) = (x, xy²2, xz) Scap: r(u, v) = (u, v, (u² − 1) (v² - 1)), Slevel: Tlevel (u, v) = (u, -v, 0), JJJ div F = 2xy +x+1, rot F = (0, -z, y²). V = {(x, y, z): -1 ≤ x ≤ +1 & div F dV= (r(x,y) = (x, y, (x² - 1) (y² - 1)) if you prefer.), −1≤ y ≤ +1 & 0 ≤ z≤r(x,y)}.

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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Asap
F(x, y, z) = (x, xy², xz)
JIJ div F dV =
div F = 2xy + x + 1,
rot F = (0, -z, y²).
Scap : r(u, v) = (u, v, (u² − 1) (v² − 1)), (r(x, y) = (x, y, (x² - 1) (3²-1)) if you prefer.),
Slevel : Tlevel (u, v) = (u, -v, 0),
V = {(x, y, z) : -1 ≤ x ≤ +1 & − 1 ≤ y ≤ +1 & 0 ≤ z ≤r(x, y)}.
Transcribed Image Text:F(x, y, z) = (x, xy², xz) JIJ div F dV = div F = 2xy + x + 1, rot F = (0, -z, y²). Scap : r(u, v) = (u, v, (u² − 1) (v² − 1)), (r(x, y) = (x, y, (x² - 1) (3²-1)) if you prefer.), Slevel : Tlevel (u, v) = (u, -v, 0), V = {(x, y, z) : -1 ≤ x ≤ +1 & − 1 ≤ y ≤ +1 & 0 ≤ z ≤r(x, y)}.
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