• Support PF! Buy your school textbooks, materials and every day products Here!

How to determine the volume of a region bounded by planes?

  • #1

Homework Statement


Let G be the region bounded by the planes x=0,y=0,z=0,x+y=1and z=x+y.

Homework Equations



(a) Find the volume of G by integration.
(b) If the region is a solid of uniform density, use triple integration to find its center of mass.

The Attempt at a Solution


[/B]
My understanding is that I need to setup a triple integral:

∫∫∫dxdydz

I’m just a little unsure about how to determine the terminals
 

Answers and Replies

  • #2
34,043
9,883
Did you draw a sketch?

You can always find boundaries for e.g. z as function of x,y and boundaries for y as function x, but sometimes there are easier methods.
 
  • #3
LCKurtz
Science Advisor
Homework Helper
Insights Author
Gold Member
9,519
734
Have you drawn a picture? That's the first step. Maybe this will help:
object.jpg
 

Attachments

  • #4
Did you draw a sketch?

You can always find boundaries for e.g. z as function of x,y and boundaries for y as function x, but sometimes there are easier methods.
So would the boundaries be:

0≤z≤x+y
0≤y≤1-x
0≤x≤1
 
  • #5
34,043
9,883
That will work.
 

Related Threads on How to determine the volume of a region bounded by planes?

Replies
2
Views
2K
Replies
3
Views
3K
Replies
5
Views
4K
  • Last Post
Replies
3
Views
3K
Replies
5
Views
3K
Replies
1
Views
238
  • Last Post
Replies
16
Views
14K
Top