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Express the integral JJ f(x, y, z)dV as an iterated integral E in six different ways, where E is the solid bounded by z = 0, z = 8y and x² = 25 - y.

Express the integral JJ f(x, y, z)dV as an iterated integral E in six different ways, where E is the solid bounded by z = 0, z = 8y and x² = 25 - y.

Advanced Engineering Mathematics
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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Express the integral f(x, y, z)dV as an iterated integral E in six different ways, where E is the solid bounded by z = 0, z = 8y and x² = 25 — y. ph,(x,y) h₁(x,y) 1. To a = b •9₂(x) 91(x) h₁(x, y) a = 91(x) b 91(y) h₁(x, y) a = rb r92 (y) •h₂(x,y) 2. [" [") h(z) f(x, y, z)dzdady 9₁ (y) h₁(x,y) = a = = 91(2): hı(y, z) b = = 92(x) ob r92(2) ph₂(y,z) 3. [³ [9(²) fhólu²) ƒ(x, y, z)dædydz 91 (2) h₁(y,z) b b 9₁(y) h₁(y, z) : |h₂(x, y) = = 92(y) f(x, y, z)dzdydx = |h₂(x, y) = ·b 92 h₂(y,z) 4. [ f(n) [²²) f(x, y, z)dzdzdy 9₁ h₁(y,z) |92(z) = = |h₂(y, z) = 92 (y) h₂(y, z) =
Transcribed Image Text:Express the integral f(x, y, z)dV as an iterated integral E in six different ways, where E is the solid bounded by z = 0, z = 8y and x² = 25 — y. ph,(x,y) h₁(x,y) 1. To a = b •9₂(x) 91(x) h₁(x, y) a = 91(x) b 91(y) h₁(x, y) a = rb r92 (y) •h₂(x,y) 2. [" [") h(z) f(x, y, z)dzdady 9₁ (y) h₁(x,y) = a = = 91(2): hı(y, z) b = = 92(x) ob r92(2) ph₂(y,z) 3. [³ [9(²) fhólu²) ƒ(x, y, z)dædydz 91 (2) h₁(y,z) b b 9₁(y) h₁(y, z) : |h₂(x, y) = = 92(y) f(x, y, z)dzdydx = |h₂(x, y) = ·b 92 h₂(y,z) 4. [ f(n) [²²) f(x, y, z)dzdzdy 9₁ h₁(y,z) |92(z) = = |h₂(y, z) = 92 (y) h₂(y, z) =
• 9₂(x) • h₂(x,z) 5. S. c) d) f(z, y, z) dydzdz a 9₁(x) h₁(x,z) a = 91(x) h₁(x, z) = a = b = = •b r92(2) ph₂(x,z) 6. 3. faste) f) f(x, y, z)dydzdz a 9₁ (2) h₁(x,z) b 91 (2) h₁(x, z) = = 92(x) = = h₂(x, z) = 92 (2) = h₂(x, z) =
Transcribed Image Text:• 9₂(x) • h₂(x,z) 5. S. c) d) f(z, y, z) dydzdz a 9₁(x) h₁(x,z) a = 91(x) h₁(x, z) = a = b = = •b r92(2) ph₂(x,z) 6. 3. faste) f) f(x, y, z)dydzdz a 9₁ (2) h₁(x,z) b 91 (2) h₁(x, z) = = 92(x) = = h₂(x, z) = 92 (2) = h₂(x, z) =
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