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

[Tom31415926535]

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

 

[mfb]

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.

 

[LCKurtz]

Have you drawn a picture? That's the first step. Maybe this will help:

 

[Tom31415926535]

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

 

[mfb]

That will work.