If f(x) is an integrable function over e...

If f(x) is an integrable function over every interval on the real line such that f(t+x)=f(x) for every x and real t, then
` int_(a)^(a+1) f(x)dx` is equal to

A

`overset(a)underset(0)int f(x)dx`

B

`overset(t)underset(0)int f(x)dx`

C

`overset(t)underset(a)int f(x)dx`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:

B

Promotional Banner

Promotional Banner

Topper's Solved these Questions

DEFINITE INTEGRALS
OBJECTIVE RD SHARMA|Exercise Chapter Test 1|60 Videos
DEFINITE INTEGRALS
OBJECTIVE RD SHARMA|Exercise Chapter Test 2|60 Videos
DEFINITE INTEGRALS
OBJECTIVE RD SHARMA|Exercise Section II - Assertion Reason Type|12 Videos
CONTINUITY AND DIFFERENTIABILITY
OBJECTIVE RD SHARMA|Exercise Exercise|86 Videos
DERIVATIVE AS A RATE MEASURER
OBJECTIVE RD SHARMA|Exercise Exercise|26 Videos

Similar Questions

Explore conceptually related problems

Given a function f(x) such that It is integrable over every interval on the real line,and f(t+x)=f(x), for every x and a real t Then show that the integral int_(a)^(a+t)f(x)dx is independent of a .

If f(x) is integrable over [1,2] then int_(1)^(2)f(x)dx is equal to

Suppose f is such that f(-x)=-f(x) for every real x and int_(0)^(1)f(x)dx=5, then int_(-1)^(0)f(t)dt=

A continous function f(x) is such that f(3x)=2f(x), AA x in R . If int_(0)^(1)f(x)dx=1, then int_(1)^(3)f(x)dx is equal to

If a is a fixed real number such that f(a-x)+f(a+x)=0, then int_(0)^(2a) f(x) dx=

Let f:R to R be continuous function such that f(x)=f(2x) for all x in R . If f(t)=3, then the value of int_(-1)^(1) f(f(x))dx , is

Let f(x) be a continuous function such that f(a-x)+f(x)=0 for all x in [0,a] . Then, the value of the integral int_(0)^(a) (1)/(1+e^(f(x)))dx is equal to

if f(x) is an odd periodic function defined on interval [-T/2,T/2], where T is the time period of f(x). Then time period of phi(x)=int_(a)^(x)f(x)dx is

Let f(x) be a differentiable function such that f(x)=x^(2)+int_(0)^(x)e^(-t)f(x-t)dt then int_(0)^(1)f(x)dx=

if f(x) is a differential function such that f(x)=int_(0)^(x)(1+2xf(t))dt&f(1)=e , then Q. int_(0)^(1)f(x)dx=

OBJECTIVE RD SHARMA-DEFINITE INTEGRALS-Exercise

If f(a+x)=f(x), then int(0)^(na) f(x)dx is equal to (n in N)
Text Solution
|
If f(t) is a continuous function defined on [a,b] such that f(t) is an...
Text Solution
|
If f(x) is an integrable function over every interval on the real line...
Text Solution
|
If I(1)=int(3pi)^(0) f(cos^(2)x)dx and I(2)=int(pi)^(0) f(cos^(2)x) th...
Text Solution
|
If f(x) is a quadratic polynomial in x such that 6int0^1 f(x)dx-{f(0...
Text Solution
|
The value of integral int(-2)^(4) x[x]dx is
Text Solution
|
If h(a)=h(b), the value of the integral inta^b [f(g(h(x))]^(-1)f'(g...
Text Solution
|
If F(x)=(1)/(x^(2))int(4)^(x) [4t^(2)-2F'(t)]dt then F'(4) equals
Text Solution
|
If f(x) is an odd function defined on [-T//2,T//2] and has period T, t...
Text Solution
|
If for every integer n, int(n)^(n+1) f(x)dx=n^(2), then the value of ...
Text Solution
|
int(-pi+4)^(pi//4) (tan^(2)x)/(1+a^(x))dx is equal to
Text Solution
|
The value of int(0)^(pi//2) cosec(x-pi//3)cosec(x-pi//6)dx is
Text Solution
|
The value of int(-1)^(1) x|x|dx, is
Text Solution
|
int0^3 |x^(3)+x^(2)+3x|dx is equal to
Text Solution
|
The value of the integral int(0)^(3) (dx)/(sqrt(x+1)+sqrt(5x+1)) is
Text Solution
|
int(1)^(-1) (x^(3)+|x|+1)/(x^(2)+2|x|+1)dxis equal to
Text Solution
|
int(-pi/2)^(pi//2) log(e ){((ax^(2)+bx+c)/(ax^(2)-bx+c))(a+b)|sinx|}dx...
Text Solution
|
For any natural number n, the value of the integral int(0)^(sqrt(n))...
Text Solution
|
For any n in R^(+), the value of the integral int(0)^(n[x]) (x-[x])d...
Text Solution
|
If phi'(x)=(log(e )|sin x|)/(x),x ne pi,n in Z and int(1)^(3) (3log(...
Text Solution
|