If f(x) be a continuous function such th...

If `f(x)` be a continuous function such that `f(x)` does not vanish for all `x in R ,a n difint_(-1)^2f(x)dx=int_1^2f(x)dx ,t h e nf(x)i s` (A) an even function (B) an odd function (C) a periodic function (D) none of these

Text Solution

AI Generated Solution

Topper's Solved these Questions

JEE MAIN
JEE MAINS PREVIOUS YEAR ENGLISH|Exercise MATH|21 Videos
LIMITS AND DERIVATIVES
JEE MAINS PREVIOUS YEAR ENGLISH|Exercise All Questions|5 Videos

Similar Questions

Explore conceptually related problems

Let f(x) be a continuous function in R such that f(x) does not vanish for all x in R . If int_1^5 f(x)dx=int_-1^5 f(x)dx , then in R, f(x) is (A) an even function (B) an odd function (C) a periodic function with period 5 (D) none of these

If f(x)={x^2sin(pix)/2,|x|<1x|x|,|x|geq1,t h e nf(x)i s an even function (b) an odd function a periodic function (d) none of these

The function f(x)=log(x+sqrt(x^(2)+1)) , is (a) an even function (b) an odd function (c ) a periodic function (d) Neither an even nor an odd function.

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

Let f(x) be a continuous function in R such that f(x)+f(y)=f(x+y) , then int_-2^2 f(x)dx= (A) 2int_0^2 f(x)dx (B) 0 (C) 2f(2) (D) none of these

Let f (x) be a conitnuous function defined on [0,a] such that f(a-x)=f(x)"for all" x in [ 0,a] . If int_(0)^(a//2) f(x) dx=alpha, then int _(0)^(a) f(x) dx is equal to

Let f:R in R be a continuous function such that f(1)=2. If lim_(x to 1) int_(2)^(f(x)) (2t)/(x-1)dt=4 , then the value of f'(1) is

Let f(x) be a continuous and periodic function such that f(x)=f(x+T) for all xepsilonR,Tgt0 .If int_(-2T)^(a+5T)f(x)dx=19(ag0) and int_(0)^(T)f(x)dx=2 , then find the value of int_(0)^(a)f(x)dx .

The function f(x)=sin(log(x+sqrt(1+x^2))) is (a) even function (b) odd function (c) neither even nor odd (d) periodic function

JEE MAINS PREVIOUS YEAR ENGLISH-JEE MAINS-All Questions

If f(x) be a continuous function such that f(x) does not vanish for al...
Text Solution
|
Find the total number of ways of selecting five letters from the word ...
Text Solution
|
If x=9 is the chord of contact of the hyperbola x^2-y^2=9 then the equ...
Text Solution
|
Solution of, (dy)/(dx)+sin[(x+y)/2]=sin[(x-y)/2] is: (A) ln|tany/2|+2s...
Text Solution
|
Given a > b >0,a1> b1>0, area of ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 is ...
Text Solution
|
The number of real roots xcosx=1 in [0,2pi] (A) 1 (B) 2 (C) 3 (D) non...
Text Solution
|
Two persons A and B agree to meet at a place between 11 and 12. The fi...
Text Solution
|
Two medians AD and BE of A B C are of length 4sqrt(2) & 6 and angle A...
Text Solution
|
The number of values of x where the function f(x)=cos x +cos (sqrt(2)x...
Text Solution
|
In [0, 1] the Lagrange's Mean Value Theorem is not applicable to: (a) ...
Text Solution
|
If vec a= hat i+ hat j+ hat ka n d vec b= hat i-2 hat j+ hat k , then...
Text Solution
|
If x=9 is the chord of contact of the hyperbola x^2-y^2=9 then the equ...
Text Solution
|
Find the value of log tan1^0logtan2^0...........logtan89^0
Text Solution
|
If |(x, x^2, x^3 +1), (y, y^2, y^3+1), (z, z^2, z^3+1)| = 0 and x ,y a...
Text Solution
|
If z lies on the circle |z-1|=1, then (z-2)/z is
Text Solution
|
Find the coordinates of a point on the (x-1)/2=(y+1)/(-3)=z atg a d...
Text Solution
|
The point of intersection of two tangents to the hyperbola (x^(2))/(a^...
Text Solution
|
prove that int1/(x(x^4+1))dx=1/4log(x^4/(x^4+1))+c
Text Solution
|
If (lim)(xvec0)[cot(pi/4+x)]^(1//x)=A e^2 then the value of A is: e^2 ...
Text Solution
|
A man is known to speak truth 3 out of 4 times. He throws a die and re...
Text Solution
|