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 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 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) = int_(-2)^(x)|t + 1|dt , then

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

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 f(x)=int_(2)^(x)f(t^(2)-3t+4)dt . Then

Given a function g, continous everywhere such that g (1)=5 and int _(0)^(1) g (t) dt =2. If f (x) =1/2 int _(0) ^(x) (x -t)^(2) g (t) dt, then find the value of f '(1)+f''(1).