In Problems 1-3, find the volume of the given solid. First, sketch the solid; then estimate its volume; finally, determine its exact volume.
1. Solid under the plane z = x + y + 1 over R = {(x, y): 0 ( x ( 1, 1 ( y ( 3}
2. Solid under the plane z = 2x + 3y and over R = {(x, y): 1 ( x ( 2, 0 ( y ( 4}
3. Solid between z = x2 + y2 + 2 and z = 1 and lying above R = {(x, y): -1 ( x ( 1, 0 ( y ( 1)