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

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

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