# 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?!?

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#### 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"

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