Let `G(x)=inte^x(int_0^xf(t)dt+f(x))dx` where `f(x)` is continuous on R. If `f(0)=1, G(0)=0` then `G(0)` equals

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 ^ 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 :

f(x)=(x^(2))/(1+x^(3));g(t)=int f(t)dt. If g(1)=0 then g(x) equals-

Let g(x) = int_0^(x) f(t) dt , where 1/2 le f(t) < 1, t in [0,1] and 0 < f(t) le 1/2 "for" t in[1,2] . Then :

Let phi(x,t)={(x(t-1),xlet),(t(x-1), tltx):} , where t is a continuous function of x in [0,1] . Let g(x)=int_0^1 f(t)phi(x,t)dt , then g\'\'(x) = (A) g(0)+g(1)=1 (B) g(0)=0 (C) g(1)=1 (D) g\'\'(x)=f(x)

Let phi(x,t)={(x(t-1),xlet),(t(x-1), tltx):} , where t is a continuous function of x in [0,1] . Let g(x)=int_0^1 f(t)phi(x,t)dt , then g\'\'(x) = (A) g(0)=1 (B) g(0)=0 (C) g(1)=1 (D) g\'\'(x)=f(x)

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 The value of g(x+2)-g(x) is equal to (A) g(1) (B) 0 (C) g(2) (D) g(3)