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
Solve lim(x->5) [x-5/|x-5|]
 
 
Ans: Hello Student, Please find answer to your question below So right hand and left hand limits are different. Limit does not exist.
  img
Jitender Singh one month ago
options 1/TT+2-A 1/2+1/(TT+2)-A 1/2-1/(TT+2)-A ½ +1/(TT+2)+A
 
 
Ans: Hello Student, Please find answer to your question below Your question is not clear and seems to be incomplete. Please recheck your question andpost it again. I am not able to interpret...
  img
Jitender Singh 28 days ago
evaluate the following integral ∫ cos 2x / (cos x + sin x)^2 dx
 
 
Ans: Hello student, Please find the answer to your question below
  img
Jitender Singh 12 days ago
integration of- 1/(1-x 2 (1-x 2 ) 1/2 )dx = ?
 
 
assume x = sin , dx = cos d so 1 – x^2 = cos^2 so integration becomes sec^2 d = tan = tan (sin-1 x)
  img
Suraj Prasad 5 days ago
hi in numerator it is e raise to power modulus of x ...please help ….i posted ….......last time i posted this quetion …..at that time i called e raise to power integral part which is wrong...
 
 
Ans: Hello Student, Please find answer to your question below So, range of f(x) varies from -1 to 1 (both exclusive). But the co-domain is R. So f(x) is into function. (Function is onto when...
  img
Jitender Singh 3 days ago
i i
 
The solution set of equation mod(1-log 1/6 x)+2=mod(3-log 1/6 x) is?
 
 
Ans: Hello Student, Please find answer to your question below Domain: x > 0 0 < x < 1/216 x > 1/6 So x should be less than 1/6.
  img
Jitender Singh 28 days ago
In a triangle root(abc(a+b+c))/area is always greater than of equal to ? less than or equal to
 
 
Hello Student, Thanks & Regards Arun Kumar Btech, IIT Delhi Askiitians Faculty
  img
Arun Kumar 2 months ago
Let P(x) =ax^2+bx+c, Q(x) =ax^2 +cx +b and R(x) =ax^2+bcx+b^3+c^3-4abc where a,b,c belongs to R and a is not equal to zero. The equation R(x) =0 will have non real roots if (A) P(x) =0 has...
 
 
Find out theDiscriminantof all the equations by using the formula . After you have found out the determinant of the given quations you will find that Discriminant of R(x)is equal to the...
  img
Sourabh Singh 4 days ago
View all Questions »