Changing the order of integration for a triple integral?

[SMA_01]

Homework Statement

[itex]\int^{1}_{0}[/itex][itex]\int^{x}_{0}[/itex][itex]\int^{y}_{0}[/itex] f(x,y,z)dzdydx

I need to write it in terms of dxdydz

Homework Equations

The Attempt at a Solution

I've tried to draw the 3D representation. I don't really know how to change the order, I don't recall my teacher even showing us this. I know how to change the order of integration for double integrals, but not this. Any help would be appreciated.

 

[Mark44]

Homework Statement

[itex]\int^{1}_{0}[/itex][itex]\int^{x}_{0}[/itex][itex]\int^{y}_{0}[/itex] f(x,y,z)dzdydx

I need to write it in terms of dxdydz

Homework Equations

The Attempt at a Solution

I've tried to draw the 3D representation. I don't really know how to change the order, I don't recall my teacher even showing us this. I know how to change the order of integration for double integrals, but not this. Any help would be appreciated.

Have you started by sketching the region of integration (not the integrand). The region as described in your first iterated integral is:
0 <= z <= y
0 <= y <= x
0 <= x <= 1
Each of these inequalities describes two boundary planes. If you rewrite your integral with a different order of integration, you'll need to come up with a different description for the same region.