Find Volume of Region: Tetrahedron Bounded by Coordinate Planes & Plane

[DWill]

Find the volume of this region: The tetrahedron in the first octant bounded by the coordinate planes and the plane passing through (1, 0, 0), (0, 2, 0), and (0, 0, 3).


Looking at this problem I thought it just involved solving a fairly simple triple integral:

||| dz dy dx

With these limits of integration:
0 <= x <= 1
0 <= y <= 2
0 <= z <= 3

I get the answer 6, but my textbook says the answer is 1. Is this a typo in the textbook or did I do something stupid?

 

[Defennder]

What are the equations of the planes which make up the tetrahedron? What you have done appears to be calculating the volume of a cuboid in the first octant of dimensions 1x2x3. That's not the shape of a tetrahedron.

 

[DWill]

Oh I see, I have to come up with the equations of the planes myself. that was stupid of me..thanks!

 

[HallsofIvy]

Using constants for limits of integration gives the volume of the rectangular solid 0 <= x <= 1, 0 <= y <= 2, 0 <= z <= 3.