Volume of Solid in First Octant: Triple Integration Problem

[aaronfue]

Homework Statement

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

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.

The Attempt at a Solution

 

[haruspex]

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]

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.