If `f(x)=int(x^8+4)/(x^4-2x^2+2)dx` and `f(0)=0,t h e n` (a)`f(x)` is an odd function (b)`f(x)` has range `R` (c)`f(x)` has at least one real root (d)`f(x)` is a monotonic function.

If f(x)= int_(x^2)^(x^(2) +4) e^(-t^(2) ) dt , then the function f(x) increases in

If f(2-x)=f(2+x),f(4+x)=f(4-x) and int_(0)^(2)f(x)dx=5 then int_(0)^(50)f(x)dx is

If |int_(a)^(b)f(x)dx|=int_(a)^(b)|f(x)|dx,a

Let f:(0,oo)vec R be given by f(x)=int_((1)/(x))^(x)(e^(-(t+(1)/(t)))dt)/(t), then (a)f(x) is monotonically increasing on [1,oo)(b)f(x) is monotonically decreasing on (1,oo)(b)f(x) is an odd function of x on R

Statement I The function f(x) = int_(0)^(x) sqrt(1+t^(2) dt ) is an odd function and g(x)=f'(x) is an even function , then f(x) is an odd function.

If int(x^(2)-x+1)/((x^(2)+1)^((3)/(2)))e^(x)dx=e^(x)f(x)+c, then f(x) is an even function f(x) is a bounded function the range of f(x) is (0,1)f(x) has two points of extrema

int_(-a)^(a)f(x)dx= 2int_(0)^(a)f(x)dx, if f is an even function 0, if f is an odd function.

Let f(x)= 3/(x-2)+4/(x-3)+5/(x-4) . Then f(x)=0 has (A) exactly one real root in (2,3) (B) exactly one real root in (3,4) (C) at least one real root in (2,3) (D) none of these