Home
Class 12
MATHS
The function f is continuous and has the...

The function `f` is continuous and has the property `f(f(x))=1-x` for all `x in [0,1]` and `J=int_0^1 f(x)dx`. Then which of the following is/are true?
(A) `f(1/4)+f(3/4)=1`
(B)`f(1/3).f(2/3)=1`
(C) the value of `J` equals to `1/2`
(D) `int_0^(pi/2) (sinxdx)/(sinx+cosx)^3` has the same value as `J`

A

`f((1)/(4))+f((3)/(4))=1`

B

`f(1/3).f(2/3)=1`

C

the value of J equals to `1//2`

D

`int_(0)^(pi//2)(sinx dx )/(sinx+ cos x)^(3)` has the value of as J

Text Solution

Verified by Experts

The correct Answer is:
A, C, D
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|17 Videos

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise (Matching Type Questions)|4 Videos

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise (Single Option Correct Type Questions)|34 Videos

  • COORDINATE SYSTEM AND COORDINATES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

  • DETERMINANTS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|18 Videos

Similar Questions

Explore conceptually related problems

The function f is continuous and has the property f(f(x))=1-x for all x in [0,1] and J=int_0^1 f(x)dx . Then which of the following is/are true? (A) f(1/4)+f(3/4)=1 (B) the value of J equals to 1/2 (C) f(1/3).f(2/3)=1 (D) int_0^(pi/2) (sinxdx)/(sinx+cosx)^3 has the same value as J

The function of f is continuous and has the property f(f(x))=1-x. Then the value of f((1)/(4))+f((3)/(4)) is

If f(x)={[-3x+2,x =1]} ,then which of the following is not true (A) f'(1^(+))=1 (B) f'(1^(-))=-3 (C) f'(1^(-))=f'(1^(+))=1 (D) f is not differentiable at x=1

If f(6-x)=f(x), for all x, then 1/5 int_2^3 x[f(x)+f(x+1)]dx is equal to :

Suppose f is continuous and satisfies f(x)+f(-x)=x^(2) then the integral int_(-1)^(1)f(x)dx has the value equal to

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

Let f(x) be a continuous function such that f(a-x)+f(x)=0 for all x in [0,a] . Then int_0^a dx/(1+e^(f(x)))= (A) a (B) a/2 (C) 1/2f(a) (D) none of these

If a continuous function f satisfies int_(0)^(f(x))t^(3)dt=x^(2)(1+x) for all x>=0 then f(2)

Let f : R to R be continuous function such that f (x) + f (x+1) = 2, for all x in R. If I _(1) int_(0) ^(8) f (x) dx and I _(2) = int _(-1) ^(3) f (x) dx, then the value of I _(2) +2 I _(2) is equal to "________"