Area bouned by the region [x]^2=[y]^2 of x belongs to [1,5] (where [.] denotes the greatest integer function)

2 years ago

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Hi Debadutta,


 


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.


 


Regards,


Ashwin (IIT Madras).

2 years ago

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