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 a real -valued function defined on the interval (-1, 1) such that e^(-x)f(x) = 2+int_(0)^(x) sqrt(t^(4) + 1)dt for all x in (-1, 1) and let f^(-1) be the inverse function of f. then show that (f^(-1)(2))^1 = (1)/(3)

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 a constant function.

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.

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: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

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