Triple integral for y dV over region bounded by plane 4x+2y+3z=16

[hils0005]

Homework Statement

W is the solid bounded by the three coordinate planes and the surface 4x+2y+3z=16, Calculate Mxz=$$\int$$$$\int$$$$\int$$ y dV

Homework Equations

The Attempt at a Solution

the surface 4x +2y +3z=16 is a plane that crosses boundries at (4,0,0), (0,8,0) and (0,0,16/3)

This is how I set up my integral but I am getting an incorrect answer...
$$\int$$$$\int$$$$\int$$ y dzdxdy
0$$\leq$$z$$\leq$$16-4x-2y
0$$\leq$$x$$\leq$$1/2(y-8)
0$$\leq$$y$$\leq$$8

can anyone tell what I'm doing wrong

 

[radicalfreedo]

your boundary.
4x+2y+3z=16
To get the y-range, set x=0, z=0, so y is between 0 and 8
for x-range, set z=0. then x is between 0 and (16-2y)/4
z goes between 0 and (16-4x-2y)/3
the crossing points are irrelavant.
try and see what u get.