# Using triple integrals

1. Apr 1, 2012

### Timebomb3750

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

Use a triple integral to find the volume of the region. Below x+2y+2z=4, above z=2x, in the first octant.

2. Relevant equations

V=∫∫∫dV=∫∫∫dxdydz

3. The attempt at a solution

I have no clue where to begin as to finding those darn limits to integrate with. I'm sure I can evaluate the integral just fine, but I need help finding limits.

2. Apr 1, 2012

### Timebomb3750

Well, after plotting those two equations into my mac grapher app, it seems my y-limits could be from 0 to 2. But I'm unsure as to finding my x and z limits.

3. Apr 1, 2012

### Timebomb3750

Any assistance would be greatly appreciated. Thanks.

4. Apr 1, 2012

### SammyS

Staff Emeritus

(Look at the rules for posting on this Forum, especially as regards "bumping" your thread.)

5. Apr 1, 2012

### SammyS

Staff Emeritus
Where do the planes, x+2y+2z=4, and, z=2x, intersect?

Where does each of those planes intersect the coordinate axes?

6. Apr 1, 2012

### Timebomb3750

Well, z=2x goes through the entire the y-axis, but doesn't intersect any other axes. x+2y+2z=4 intersects axes at x=4, y=2, and z=2.

The two planes intersect at 2y+5x=4.

But what's your point? What do I get out of this?

7. Apr 1, 2012

### SammyS

Staff Emeritus
I should have asked, "Where does each of those planes intersect the coordinate planes?"

The intersection of the two planes is a line. The equation, 2y+5x=4, specifies a plane !