# 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

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#### haruspex

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)

#### haruspex

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.

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