integration

[tallman2366]

Hello
Determine the volume of the solid bounded by the planes z+y+2x=4 , x=0, y=0, z=0
In the positive 1st octant

This is the work that I have done
i know that z=0. so z+y+2x=4 so z= 4-y-2x
0 = 4 -y-2x
so is z is bounded between 0 and 4-y-2x. so the limits of integration for z are 0 and 4-y-2x
I am trying to draw the region so I can figure out the other limits of integration.
Not sure how to graph the region . Thank you for you rhelp
Pat

 

[tallman2366]

I know what the region looks like, its a triangle that intersects (0,3) and (1.5,0)
not sure what my limits of integration would be for the x and y though

 

[Steven G]

Please don't say that z=0 when you know (and said!) that z= 4-y-2x. Is 4-y-2x always 0?

What does it mean when you say it is a triangular region that intersects at (0,3) and (1.5,0)?