# Triple Integration for Volume

#### aaronfue

1. Homework Statement

Find the volume of the solid in the first octant bounded by the graphs of:
z=1-y2
y=2x
x=3

2. Homework Equations

I was able to graph all three but I can't picture the region for integration. I'm not sure if I even have to graph it or if I can get my limits without the graph.

3. The Attempt at a Solution

Last edited:
Related Calculus and Beyond Homework Help News on Phys.org

#### haruspex

Science Advisor
Homework Helper
Gold Member
2018 Award
Please post an attempt at writing out the integral.

#### aaronfue

After graphing the equations, I came up with:

$\int^{1}_{-1}$ $\int^{3}_{0}$ $\int^{1}_{0}$ dzdxdy (this order was given as a hint)

My final answer was 6?

#### haruspex

Science Advisor
Homework Helper
Gold Member
2018 Award
No, you need to put the given constraints as bounds in the integrals. The order needed also results from the dependencies in those bounds. The y bounds depend on x, and the z bounds depend on y, and therefore on x too. So the order should be z, y, x.

### 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