Trouble with multivariable limits of integration on Ti89

[aufbau86]

Hello,

I'm currently trying to get my Ti-89 Titanium to compute the following triple integral;

f(x,y,z) = xy(1-z) where 0<x<1, 0<y<1, 0<z<1, and x+y+z<1

int(int(int(f(x,y,z),x,0,1-y-z),y,0,1-z),x,0,1)

The problem is that I can't get my Ti89 to substitute in for the limits of integration properly. For example, here is the result I get back after computing only the inner integral;

int(f(x,y,z),x,0,1-y-z) = -xy(1-z)(y+z-1)

It seems that it's holding the entire function constant whenever it has to interpret an integral at a limit which includes other variables. Basically it does this;

int(C,x,0,1-y-z) = C*int(1,x,0,1-y-z)
where C = Constant = f(x,y,z)

I've been trying to get it to work for a couple of infuriating hours, so I'm hoping one of you wizards can let me know how to get it to properly interpret integrals with multivariable limits of integration.

Thanks!

 

[ArcanaNoir]

I don't have a TI-89, but try this http://www.mathcs.citadel.edu/~chenm/231.dir/07sp.dir/lect13_calculator_1.pdf