the value of integrand limit [0 to [x]] {x-[x]}dx (where [.] denotes greatest integer function.

2 years ago

Share

Answers : (2)

                                        

Arun Kumar
IIT Delhi
Askiitians Faculty
5 months ago
                                        
x-[x] is periodic with period 1. therefore, ?0[x]x-[x] dx = [x]?01x-[x] dx =[x]/2
we can get integral of x-[x] within limits 0 and 1 using method of areas as ½.
Therefore the answer is [x]/2
5 months 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
Integrate ∫(1+cos4x)/(cotx – tanx) dx
 
 
Ans: Hello Student, Please find answer to your question below
  img
Jitender Singh 2 months ago
evaluate ∫ 2 cos^2 x- cos 2x / cos^2 x dx
 
 
Ans: Hello Student, Please find answer to your question below
  img
Jitender Singh 2 months ago
evaluate ∫(5cos^3(x) + 6sin^3(x)) / 2sin^2(x) cos^2(x) dx
 
 
Ans: Hello Student, Please find answer to your question below
  img
Jitender Singh one month ago
Find no. of solutions of the equation 16^(sin^x) + 16^(cos^x) = 10, where 0
 
 
Dear student, please check the attached file.
  img
Sunil Raikwar 2 months ago
If m>1, then sum of the nth power of n even number is
 
 
Hello Student, You can do this by Faulhaber's formula. Thanks & Regards Arun Kumar Btech, IIT Delhi Askiitians Faculty
  img
Arun Kumar 3 months ago
find sum 1^2*C1+3^2*C3+5^2*C5....
 
 
Hello Student, Thanks & Regards Arun Kumar Btech, IIT Delhi Askiitians Faculty
  img
Arun Kumar 3 months ago
View all Questions »