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

2 years ago

Share

Answers : (1)

                    

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

Post Your Answer

More Questions On Integral Calculus

Ask Experts

Have any Question? Ask Experts
Post Question
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!!
Click Here for details