f is a real valued function from R to R such that `f(x)+f(-x)=2`, then `int_(1-x)^(1+X)f^(-1)(t)dt=`

Let f be real-valued function such that f(2)=2 and f'(2)=1 then lim_(x rarr2)int_(2)^(f(x))(4t^(3))/(x-2)backslash dt is equal to :

Let f be a real-valued function satisfying f(x)+f(x+4)=f(x+2)+f(x+6) Prove that int_(x)^(x+8)f(t)dt is constant function.

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=

Let f be a real-valued function on the interval (-1,1) such that e^(-x) f(x)=2+underset(0)overset(x)int sqrt(t^(4)+1), dt, AA x in (-1,1) and let f^(-1) be the inverse function of f. Then [f^(-1) (2)] is a equal to:

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=

Let f:R to R be defined as f(x)=e^(-x)sinx . If F:[0, 1] to R is a differentiable function such that F(x)=int_(0)^(x)f(t)dt , then the vlaue of int_(0)^(1)(F'(x)+f(x))e^(x)dx lies in the interval

If f(x) is real valued function such that (f(x-1)+f(x+1))/(2f(x))=sin60^(@),AA x in R then find the value of f(x-1)+f(x+5)

Let f:R rarr R be a differentiable and strictly decreasing function such that f(0)=1 and f(1)=0. For x in R, let F(x)=int_(0)^(x)(t-2)f(t)dt