Let f(x)=max. {x+|x|,x-[x]} , where [x] ...

Let `f(x)=max. {x+|x|,x-[x]}` , where [x] denotes the greatest integer less than or equal to x, then `int_(-2)^(2) f(x)` is equal to

A

3

B

5

C

1

D

none of these

Text Solution

Verified by Experts

The correct Answer is:

B

Since `x+|x|gtx-[x]"for all" x gt0` and `x+|x|=0 le x -[x] "for all" x lt0`
`:.underset(-2)overset(2)int f(x)dx=underset(-2)overset(0)int (x-[x])dx+underset(0)overset(2)int (x+x|)dx`
`rArrunderset(-2)overset(2)int f(x)dx=2xx(1)/(2)+underset(0)overset(2)int 2xx =1+4=5`

Promotional Banner

Promotional Banner

Topper's Solved these Questions

DEFINITE INTEGRALS
OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|12 Videos
DEFINITE INTEGRALS
OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|143 Videos
DEFINITE INTEGRALS
OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test 2|56 Videos
CONTINUITY AND DIFFERENTIABILITY
OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|87 Videos
DERIVATIVE AS A RATE MEASURER
OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|26 Videos

Similar Questions

Explore conceptually related problems

If f(x)=|x-1|-[x] , where [x] is the greatest integer less than or equal to x, then

Let [x] denote the greatest integer less than or equal to x . Then, int_(0)^(1.5)[x]dx=?

Let [x] denotes the greatest integer less than or equal to x and f(x)=[tan^(2)x] . Then

Let f(x)=[x]+[-x] , where [x] denotes the greastest integer less than or equal to x . Then, for any integer m

Examine Lim_(xto 2) [ x] , where [ x] denotes the greatest integar less than or equal to x.

Let f(x)=[x^(2)]+[x+2]-8 , where [x] denotes the greater integer than or equal to x , then

Solve the equation x^(3)-[x]=3 , where [x] denotes the greatest integer less than or equal to x .

lim_(xrarr oo) (log[x])/(x) , where [x] denotes the greatest integer less than or equal to x, is

If f(x)=|x|+[x] , where [x] is the greatest integer less than or equal to x, the value of f(-2.5)+f(1.5) is

Lim x tending 5f(x) = (x^2-9x+20)/(x-[x]) where [x] denotes greatest integer less than or equal to x ), then

OBJECTIVE RD SHARMA ENGLISH-DEFINITE INTEGRALS-Section I - Solved Mcqs

Let f(x) be a function defined by f(x)=int(1)^(x)t(t^(2)-3t+2)dt,1ltxl...
Text Solution
|
If int(0)^(x){t}dt=int(0)^({x})t dt ("where" x gt0 neZ and and {*} rep...
Text Solution
|
Let f(x)=max. {x+|x|,x-[x]} , where [x] denotes the greatest integer l...
Text Solution
|
rArrint(0)^(oo) [(2)/(e^(x))]dx (where [*] denotes the greatest intege...
Text Solution
|
Ifint0^1(e^t dt)/(t+1)=a ,t h e ne v a l u a t eint(b-1)^b(e^(-t)dt)/(...
Text Solution
|
Evaluate: int(-1)^4f(x)dx=4a n dint2^4(3-f(x))dx=7, then find the val...
Text Solution
|
For x epsilonR, and a continuous function f let I(1)=int(sin^(2)t)^(1+...
Text Solution
|
int(1)^(4) log(e)[x]dx equals
Text Solution
|
If [.] denotes greatest integer function, then the value of int(-pi//2...
Text Solution
|
int(0)^(100pi)(sum(r=1)^(10)tanrx)dx is equal to
Text Solution
|
If I(1)=int(0)^(pi//2) cos(sin x) dx,I(2)=int(0)^(pi//2) sin (cos x)...
Text Solution
|
For any n in N, the value of the intergral int(0)^(pi) (sin 2nx)/(sin...
Text Solution
|
For any n in N, int(0)^(pi) (sin^(2)nx)/(sin^(2)x)dx is equal to
Text Solution
|
For any n in N, int(0)^(pi) (sin (2n+1)x)/(sinx)dx is equal to
Text Solution
|
If int(n)=int(-pi)^(pi)(sin nx)/((1+pi^(x))sinx) dx, n=0,1,2,………. then
Text Solution
|
If I(n)=int(0)^(pi//4) tan^(n)x dx, then (1)/(I(2)+I(4)),(1)/(I(3)+I...
Text Solution
|
Let f(x) be a function defined on R satisfyin f(x) =f(1-x) for all x...
Text Solution
|
Evaluate: 5050(int0 1(1-x^(50))^(100)dx)/(int0 1(1-x^(50))^(101)dx)
Text Solution
|
If f and g are continuous functions on [ 0, pi] satisfying f(x) +f(pi...
Text Solution
|
If f(x) and g(x) are two continuous functions defined on [-a,a] then t...
Text Solution
|