Help Integrating Tripple Integral for x+y+z=1

[Alem2000]

the question is "evaluate \iiint z \,dv, of a solid tetrahedron bounded by the four planes x=0,y=0,z=0, and x+y+z=1"
I can set up the problem correctly but i can't seem to integrate it right
\int_{0}^1 \int_{0}^{1-x} \int_{0}^{1-x-y} z dzdydx
(1/2) \int_{0}^1 \int_{0}^{1-x} (1-x-y)^2dydx
can somone please show me the last few steps of this problem?

 

[dextercioby]

Open the brackets and integrate each term with corresponding limits...

Daniel.

 

[arildno]

For the evaluation of the inner integral, use the y-anti-derivative :
-\frac{1}{3}(1-x-y)^{3}