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
3 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
3 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
evaluate the following integral ∫ a / b + ce^x dx
 
 
Ans: Hello student, Please find the answer to your question below
  img
Jitender Singh 14 days ago
Solve pls ∫tan -1 (1-x+x 2 ) dx Limit if from 0 to 1.
 
 
Ans: Hello Student, Please find answer to your question below
  img
Jitender Singh one month ago
options -nTT -(n +1) π -2nT -2(n +1) TT
 
 
Ans: Hello Student, Please find answer to your question below [sint] is a periodi with a period of 2pi.
  img
Jitender Singh one month ago
The lines y = -3/2 x and y = - 2/5x intersect the curve 3x 2 + 4xy + 5y 2 – 4 = 0 at the points P and Q respectively. The tangents drawn to the curve at P and Q: options Intersect each other...
 
 
Ans: Hello Student, Please find answer to your question below Differentiate Slope of the tangent at intersection by Parallel to x-axis. Slope of the tangent at intersection by Parallel to...
  img
Jitender Singh 29 days ago
integrate, ∫ X X dx
 
 
Ans: Hello Student, Please find answer to your question below There is not any standard mathematical expression for this integral. What we can do is expand the integral function around zero...
  img
Jitender Singh one month ago
"a relation R is defined from a set A={2,3,4,5} to a set B={3,6,7,10} as follow:"(x,y) belong to R and x is relatively prime to y . determine its range and domain“
 
 
according to given relation , (x,y) belong to R and x is relatively prime to y . determine its range and domain“ for x=2 , y= 3,7 x=3, y= 4,5 x=4 , y=3,5 x=5 , y= 2,3,4
  img
Sher Mohammad 2 months ago
Sir Pls prove that the vector area of a triangle whose vertices are a vector bvector and cvector is 0.5(bvec cross cvector +cvector cross a vec+ a vector cross b vector) Thanks and Rgds, Jai
 
 
Let A be the endpoint of , B be the endpoint of vector , and C be the endpoint of vector . Then the vector from A to B is , and the vector from A to C is . So (1/2) | X | is the area of the...
  img
bharat bajaj 2 months ago
 
Dear student, Let the vertices be given by the vectors: So, the area would be given by: Regards Sumit
  img
Sumit Majumdar 2 months ago
vectors in detail
 
 
Vectors This is a vector: A vector has magnitude (how long it is) and direction : The length of the line shows its magnitude and the arrowhead points in the direction. You can add two...
  img
ruchi yadav 6 months ago
View all Questions »