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
Solve this ∫(xsinx/e x +1) dx Limit is from -1 to 1.
 
 
Ans: Hello Student, Please find answer to your question below
  img
Jitender Singh 9 days ago
evaluate ∫ (sqrt(x)( ax^2 + bx + c)) dx
 
 
∫ (sqrt(x)( ax^2 + bx + c)dx =​∫ (x^1/2(ax^2 +bx +c)dx =​∫ (ax^5/2 +bx^3/2 +cx^1/2)dx =2​ax^7/2 /7 +2bx^5/2 /5 +2cx^3/2 /3 +K {we know that​∫x^ndx =(x^(n+1) /(n+1)} Here K is...
  img
Sunil Raikwar 5 days ago
 
make ax 2 +bx+c in to form of a((x-b/2) 2 +(c -b 2 /4)). then put (x-b/2)=(c-b 2 /4)^.5*tany. then integrate it. simple
 
Karthick vel 4 days ago
options 0 1 2 4
 
 
Ans: Hello Student, Please find answer to your question below Option (1) is correct.
  img
Jitender Singh 23 hours ago
If sinx+siny=root3(cosy-cosx) Prove that sin3x+sin3y=0.
 
 
Hello students, please check the solution of your question given below: sinx+siny = root3 ( cosx-cosy) 2sin(x+y/2)cos(x-y/2) = root3 {2sin(x+y/2)sin(y-x/2)} sin(x+y/2)[cos(x-y/2)-root3....
  img
Sunil Raikwar 2 days ago
 
Dear student, According to the given relation, we would have: If we multiply both sides by a factor of 4, we get: This on simplifying gives us: If the right hand side can be simplified to...
  img
Sumit Majumdar yesterday
the vector sum of forces 10N aand 6N can be: a)2N b)8N c)18N d)20N
 
 
answer:(b) 10-6=<vector sum=<10+6
 
Chetan Mandayam Nayakar one year ago
 
the vector can be 8 i.e option -b
 
sarvjeet kumar one year ago
 
b)8N ANS
 
Akash Kumar Dutta one year ago
Given two points a = (-2,0) and b =(0,4 ) the coordinate of a point M lying on the line 2x-3y=9 so that permeter of triangle amb is least , is
 
 
GIVEN QUESTION CAN BE SOLVED USING A.M-G.M INEQUALITY FOR PERIMETER TO BE MINIMUM AM +BM SHOULD BE MINIMUM i.e AM=BM OR SIMPLY M LIES ON PERPENDICULAR BISECTOR OF AB AND LINE2x-3y=9 i.e...
 
siddharth gupta one month ago
View all Questions »