a point P moves in x-y plane in such a way that [x+y+1]=[x] and x belongs to (0,2).

find area of the region representing all possible positions of point P is___________

(here [ ] represents greatest integer function)

The area is shown in shaded region

For 0<x<1 :

[x] = 0

so [x+y+1] shld be 0  i.e.,        0<x+y+1<1

x+y<0 and x+y+1>0

For 1<x<2 :

[x] = 1

so [x+y+1] shld be1  i.e.,        1<x+y+1<2

x+y>0 and x+y<1

Area of shaded regions is 2 sq.units