Home
Class 12
MATHS
[x] denote the greatest integer function...

[x] denote the greatest integer function.
The value of `int_(1)^(a)[x]f^(')(x)dx,agt1` is-

A

`af([a])-{f(1)+f(2)+...+f(a)}`

B

`af(a)-{f(1)+f(2)+...+f([a])}`

C

`[a]f(a)-{f(1)+f(2)+...+f([a])}`

D

`[a]f([a])-{f(1)+f(2)+...+f(a)}`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRAL

    CHHAYA PUBLICATION|Exercise SAMPLE QUESTIONS FOR COMPETITIVE EXAMINATION ( ASSERTION-REASON TYPE )|2 Videos
  • DEFINITE INTEGRAL

    CHHAYA PUBLICATION|Exercise SAMPLE QUESTIONS FOR COMPETITIVE EXAMINATION ( INTEGER ANSWER TYPE )|5 Videos
  • COORDINATE GEOMETRY

    CHHAYA PUBLICATION|Exercise JEE Advanced Archive (2016)|3 Videos
  • DEFINITE INTEGRAL AS AN AREA

    CHHAYA PUBLICATION|Exercise Assertion-Reason Type|2 Videos

Similar Questions

Explore conceptually related problems

Let f(x)="max"{x+|x|,x-[x]} , where [x] denotes the greatest integer lex . Then the value of int_(-3)^(3)f(x)dx is-

If f(x) =cos [pi^(2)]x+ cos [-pi^(2)] x, where [x] denots the greatest integer function, then the value of f((pi)/(2)) is-

[x] denote the greatest integer function. int_(0)^(pi)[cosx]dx is equal to-

The greatest integer function f(x)=[x] is -

If f : R to [-1, 1] , where f(x)=sin(pi/2[x]) (where [.] denotes the greatest integer function), then the range of f(x) is

Let f(x)={1+|x|,x<-1 [x],xgeq-1 , where [.] denotes the greatest integer function. The find the value of f{f(-2.3)}dot

If [x] denotes the greatest integer lex and n inN then value of I_n=int_0^(n^2) [sqrtx]dx is

[x] denote the greatest integer function. int_(0)^(50)sin{x-[x]pi}dx is equal to-

I=int_0^2x[2x]dx where [.] denotes the greatest integer function then the value of 16/17I must be

If f(x)=cos |x|+[|sin x/2|] (where [.] denotes the greatest integer function), then f (x) is