Homework Help: Triple Integration for Volume

1. Nov 18, 2012

aaronfue

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

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

2. Relevant 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: Nov 18, 2012
2. Nov 18, 2012

haruspex

Please post an attempt at writing out the integral.

3. Nov 18, 2012

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)

4. Nov 19, 2012

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.