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
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: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:• 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) =
Expert Solution
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