Triple Integral

  • Thread starter squenshl
  • Start date
  • #1
479
4
Given the triple integral [tex]\int\int\int_{G}[/tex] xyz dV
Where G is the region bounded by x=1, y=x, y=0, z=0, z=2.
How do I evaluate it.
Please help.
 

Answers and Replies

  • #2
daniel_i_l
Gold Member
867
0
First of all, is there any other constraint on x? I'll assume that x>=0.
Do you know how to change triple integrals into single-variable integrals?
The general idea is to first evaluate the integral while pretending that 2 of the variables are constant. Then you use that result to integrate over the other variables.

In this case it might be easiest to first evaluate the integral in the triangle 0<=x<=1 and
0<=y<=x while assuming that z is constant. Then integrate that result with z as a variable from 0 to 2. The triangle can be evaluated in a similar way. In other words:
[tex]I = \int^{2}_{0}(\int^{1}_{0}(\int^{1-x}_{0} xyz dy)dx)dz[/tex]
 
  • #3
479
4
Cheers. I got an answer of 1/3
 

Related Threads on Triple Integral

  • Last Post
Replies
0
Views
1K
  • Last Post
Replies
2
Views
982
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
5
Views
7K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
5
Views
4K
  • Last Post
Replies
8
Views
7K
Top