Let `g(x)=int_0^x f(t).dt`,where f is such that `1/2<=f(t)<=1` for `t in [0,1]` and `0<=f(t)<=1/2` for `t in [1,2]`.Then g(2) satisfies the inequality

Let g(x)=int_(0)^(x)f(t)dt where fis the function whose graph is shown.

Let f ( x) = int _ 0 ^ x g (t) dt , where g is a non - zero even function . If f(x + 5 ) = g (x) , then int _ 0 ^ x f (t ) dt equals :

Let f(x)=int_(0)^(1)|x-t|dt, then

Let f(x) = int_(0)^(x)|2t-3|dt , then f is

If _(0)^(x)sin(f(t))dt=(x+2)int_(0)^(x)t sin(f(t))dt, wherex >0 then show that f'(x)cot f(x)+(3)/(1+x)=0

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 G(x)=int e^(x)(int_(0)^(x)f(t)dt+f(x))dx where f(x) is continuous on R. If f(0)=1,G(0)=0 then G(0) equals