Volumes with triple integrals, aka I suck at geometry

Gauss M.D.

1. The problem statement, all variables and given/known data

Calculate the volume of the body that is bounded by the planes:

x+y-z = 0
y-z = 0
y+z = 0
x+y+z = 2

2. Relevant equations

3. The attempt at a solution

u = y+z
v = y-z
w = x

which gave me the new boundaries

u+w = 2
v+w = 0
v = 0
u = 0

Problem is, I must have slept late the day they taught this is class. What do I do to determine which way these inequalities go?!?

Related Calculus and Beyond Homework News on Phys.org

Mandelbroth

1. The problem statement, all variables and given/known data

Calculate the volume of the body that is bounded by the planes:

x+y-z = 0
y-z = 0
y+z = 0
x+y+z = 2
Do you think you need calculus?

$$z=x+y \\ z= -x -y +2 \\ z=y \\ z=-y$$

That should be pretty simple...:tongue:

verty

Homework Helper
You should not change variables before you have set up the integral. Do that first.

haruspex

Homework Helper
Gold Member
2018 Award
To get an idea of the shape, try to find the vertices.

"Volumes with triple integrals, aka I suck at geometry"

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving