Let `f:[1,oo]` be a differentiable function such that `f(1)=2.` If `6int_1^xf(t)dt=3xf(x)-x^3` for all `xgeq1,` then the value of `f(2)` is

Let f[1, infty) to [2, infty) be a differentiable function such that f(1) =1/3 . If 6 int_(1)^(x) f(t) dt = 3x f(x) -x^(3) for all x ge 1 , then the value of 3f(2) is

Let f(x) be a differentiable function such that f(x)=x^2 +int_0^x e^-t f(x-t) dt then int_0^1 f(x) dx=

Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x for all x in (0,oo) and f(1)=1 , then

Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x for all x in (0,oo) and f(1)=1 , then f(x) is

If f(x) is differentiable function such that int_0^xf(t)dt=((f(x))^2)/2 for all x and f(2)!=0, then value of f ' (2) is a. 3 b. 1 c. 2 d. -1 e. -2

Let f:[0,oo)->R be a continuous strictly increasing function, such that f^3(x)=int_0^x t*f^2(t)dt for every xgeq0. Then value of f(6) is_______

Let f:[0,oo) to R be a continuous strictly increasing function, such that f^3(x)=int_0^x tdotf^2(t)dt for every xgeq0. Then value of f(6) is_______

Let f(x) be a differentiable function such that int_(t)^(t^(2))xf(x)dx=(4)/(3)t^(3)-(4t)/(3)AA t ge0 , then f(1) is equal to

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

if f(x) is a differential function such that f(x)=int_(0)^(x)(1+2xf(t))dt&f(1)=e , then Q. int_(0)^(1)f(x)dx=