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Area bouned by the region [x]^2=[y]^2 of x belongs to [1,5] (where [.] denotes the greatest integer function)
Let 1≤x<2. So [x] = 1.
And [y]^2 = 1 or [y] = ± 1.
means 1≤y<2 or -1≤y<0.
So in this region you will have two squares each of area 1 unit.
So when 1≤x<2 the area will be 2 sq units.
Similarly when 2≤x<3 the area = 2 sq untis
And 3≤x<4, area = 2 sq untis.
and 4≤x<5, area = 2 sq units.
So total area in the region would be 2+2+2+2 = 8 sq untis.
Ashwin (IIT Madras).