Help with a triple integral

[OrangeOne]

Hello!

Ive been staring at this task for hours and would really appreciate if someone had a look at this:

Calculate:

? z dV
k

where k is the area which is limited by the surfaces :
x= 0
y= 0
z=0
x+y=1
x+y-z=0

I dont understand how the area looks and which "limits" to set!

Thanks in advance.

 

[galactus]

The region is bounded by the planes z=0 and z=x+y.

It is bounded in the xy plane by y=0 and y=1-x.

\(\displaystyle \int_{0}^{1}\int_{0}^{1-x}\int_{0}^{x+y}z \;\ dzdydx\)