Let `f` be a derivable function on `[0, 3]` such that `f'(x) leq 1 AA x in [0,3]` where `f(0)=0 & f(3)=3` then `f(1)=`

Let f(x) be a function defined on R such that f'(x)=f'(3-x)AA x in[0,3] with f(0)=-32 and f(3)-46 Then find the value of int_(0)^(3)f(x)dx

Let f(x) be a differentiable function satisfying f(y)f(x/y)=f(x) AA , x,y in R, y!=0 and f(1)!=0 , f'(1)=3 then

Let 'f is a function, continuous on [0,1] such that f(x) leq sqrt5 AA x in [0,1/2] and f(x) leq 2/x AA x in [1/2,1] then smallest 'a' for which int_0^1 f(x)dx leq a holds for all 'f' is

Let f(x) be a differentiable function satisfying f(y)f((x)/(y))=f(x)AA,x,y in R,y!=0 and f(1)!=0,f'(1)=3 then

Let f (x) be function defined on [0,1] such that f (1)=0 and for any a in (0,1], int _(0)^(a) f (x) dx - int _(a)^(1) f (x) dx =2 f (a) +3a +b where b is constant. int _(0)^(1) f (x) dx =

Let f (x) be function defined on [0,1] such that f (1)=0 and for any a in (0,1], int _(0)^(a) f (x) dx - int _(a)^(1) f (x) dx =2 f (a) +3a +b where b is constant. The length of the subtangent of the curve y= f (x ) at x=1//2 is:

Let f (x) be function defined on [0,1] such that f (1)=0 and for any a in (0,1], int _(0)^(a) f (x) dx - int _(a)^(1) f (x) dx =2 f (a) +3a +b where b is constant. The length of the subtangent of the curve y= f (x ) at x=1//2 is:

The function f (x) satisfy the equation f (1-x)+ 2f (x) =3x AA x in R, then f (0)=