Example Evaluate the triple integral xyz-dv, where B is the rectangular box given below. B = = {(x, y, z) | 0 ≤ x ≤ 1, −1 ≤ y ≤ 2, 0 ≤ z ≤ 5 ≤5} Solution We could use any of the six possible orders of integration. If we choose to integrate with respect to x, then y, and then z, we obtain the following. [[[x -6² - 66,0 = 1²1² 12²2² 04 0² dy dz -1) = 6³ | - [³ 32² dz Jo xyz²dV = 6 ²₁ f² xyz²dxc I dy dz = 2 <= 1 x = 0 Jy = -1 dz dy dz
Example Evaluate the triple integral xyz-dv, where B is the rectangular box given below. B = = {(x, y, z) | 0 ≤ x ≤ 1, −1 ≤ y ≤ 2, 0 ≤ z ≤ 5 ≤5} Solution We could use any of the six possible orders of integration. If we choose to integrate with respect to x, then y, and then z, we obtain the following. [[[x -6² - 66,0 = 1²1² 12²2² 04 0² dy dz -1) = 6³ | - [³ 32² dz Jo xyz²dV = 6 ²₁ f² xyz²dxc I dy dz = 2 <= 1 x = 0 Jy = -1 dz dy dz
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Example
Evaluate the triple integral
Solution
=
B = {(x, y, z) | 0 ≤ x ≤ 1, -1 ≤ y ≤ 2,0 ≤ z ≤.
5
We could use any of the six possible orders of integration. If we choose to integrate with respect to x, then y, and then z, we obtain the following.
5 (2
'1
[[] xy²² dv = [² [²₁₂ 6²
xyz²dv
5
-6²11
=
*5 2
=
5 2
yz²
= √³ 1² v²2² dy dz
(-1)
||
JJ -
5
xyz²dV, where B is the
3z
/0 4
dz
xyz²dx dy dz
15
1x=1 dy
x = 0
1y = 2
1=²
Jy = -1
rectangular box given below.
dz
dy dz](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8dcf1ee6-56c0-456c-a4b6-eb6b48ebd678%2Fd31635dd-11dc-4335-8deb-4ae964865318%2F6fkqs59_processed.png&w=3840&q=75)
Transcribed Image Text:Example
Evaluate the triple integral
Solution
=
B = {(x, y, z) | 0 ≤ x ≤ 1, -1 ≤ y ≤ 2,0 ≤ z ≤.
5
We could use any of the six possible orders of integration. If we choose to integrate with respect to x, then y, and then z, we obtain the following.
5 (2
'1
[[] xy²² dv = [² [²₁₂ 6²
xyz²dv
5
-6²11
=
*5 2
=
5 2
yz²
= √³ 1² v²2² dy dz
(-1)
||
JJ -
5
xyz²dV, where B is the
3z
/0 4
dz
xyz²dx dy dz
15
1x=1 dy
x = 0
1y = 2
1=²
Jy = -1
rectangular box given below.
dz
dy dz
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