Let f be a differentiabel function satisfying `int_(1)^(f(x))f^(-1)(t)dt=(1)/(3)(x^((3)/(2))-8)AA x>0` and f(1)=0, Then the value of f(9) is

Let f be a differentiable function satisfying int_(0)^(f(x))f^(-1)(t)dt-int_(0)^(x)(cost-f(t)dt=0 and f((pi)/2)=2/(pi) The value of lim_(x to 0)(cosx)/(f(x)) is equal to where [.] denotes greatest integer function

Let f be a differentiable function satisfying int_(0)^(f(x))f^(-1)(t)dt-int_(0)^(x)(cost-f(t)dt=0 and f((pi)/2)=2/(pi) The value of int_(0)^(pi//2) f(x)dx lies in the interval

Let f:RtoR be a differntiable function satisfying f(x)=x^(2)+3int_(0)^(x)e^(-t^(3)).f(x-t^(3))dt . Then find f(x) .

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

Let f:(0,oo)rarr(0,oo) be a differentiable function satisfying,x int_(x)^(x)(1-t)f(t)dt=int_(0)^(x)tf(t)dtx in R^(+) and f(1)=1 Determine f(x)

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 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 be a continuous function satisfying the equation int_(0)^(x)f(t)dt+int_(0)^(x)tf(x-t)dt=e^(-x)-1 , then find the value of e^(9)f(9) is equal to…………………..

Let f be a differentiable function satisfying f(x+2y)=2yf(x)+xf(y)-3xy+1 AA x , y in R such that f'(0)=1 ,then value of f(8) is equal

Let f be a twice differentiable function on R and satisfying f''(x)=(x^(2)+1)^((-3)/(2))AA x in R .If f'(0)=0 and f(1)=sqrt(2)+1 then int_(0)^(1)f(x)dx =