Let a function `f` be even and integrable everywhere and periodic with period 2. Let `g(x)=int_0^x f(t) dt` and `g(t)=k`The value of `g(x+2)-g(x)` is equal to (A) `g(1)` (B) `0` (C) `g(2)` (D) `g(3)`

Let a function f be even and integrable everywhere and periodic with period 2. Let g(x)=int_0^x f(t) dt and g(t)=k For what value of g in terms of k is

Let a function f be even and integrable everywhere and periodic with period 2. Let g(x)=int_0^x f(t) dt and g(t)=k The value of g(2) in terms of k is equal to (A) k (B) 2k (C) 3k (D) 5k

Given an even function f defined and integrable everywhere and periodic with period 2 . Let g(x)=int_0^x f(t) dt and g(t)=k for what values of g in terms of k

Let f(x) be an odd continuous function which is periodic with period 2. if g(x)=underset(0)overset(x)intf(t)dt , then

Let f(x) be a periodic function with period int_0^x f(t+n) dt 3 and f(-2/3)=7 and g(x) = .where n=3k, k in N . Then g'(7/3) =

Let f(x)=f(a-x) and g(x)+g(a-x)=4 then int_0^af(x)g(x)dx is equal to (A) 2int_0^af(x)dx (B) int_0^af(x)dx (C) 4int_0^af(x)dx (D) 0

If g(x)=int_(0)^(x)cos^(4)t dt, then g(x+pi) equals to (a) (g(x))/(g(pi)) (b) g(x)+g(pi) (c) g(x)-g(pi) (d) g(x).g(pi)

Let f(x) be a function satisfying f\'(x)=f(x) with f(0)=1 and g(x) be the function satisfying f(x)+g(x)=x^2 . Then the value of integral int_0^1 f(x)g(x)dx is equal to (A) (e-2)/4 (B) (e-3)/2 (C) (e-4)/2 (D) none of these

Let f(x)=int_2^x (dt)/sqrt(1+t^4) and g be the inverse of f . Then, the value of g'(0) is

Let g(x)=int_0^(e^x) (f\'(t)dt)/(1+t^2) . Which of the following is true?