23. Let S be the closed solid in R³ bounded by the planes x = 0, y = 0, z = 0, 2x + y = 2, and x + 2y + z = 6. What is the volume of S?

Since the volume is in the first octant this given by the area under the curve z = 6 – x – 2y where y goes from 0 to (2 – 2x) and x goes from 0 to 1 on the xy-plane. Thus, the volume is,