Let `f:R rarr R` be a differentiabe function satisfying `f(x)=x^(2)+3int_(0)^(x^(1/3))e^(-t^3)t^(2)*f(x-t^(3))dt` Then find `f(x)` is

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(x) be a differentiable function satisfying f(x)=int_(0)^(x)e^((2tx-t^(2)))cos(x-t)dt , then find the value of f''(0) .

if f be a differentiable function such that f(x) =x^(2)int_(0)^(x)e^(-t)f(x-t). dt. Then f(x) =

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 be a differentiable function such that f(x)=x^(2)+int_(0)^(x)e^(-t)f(x-t)dt then prove that f(x)=(x^(3))/(3)+x^(2)

If f(x) is differentiable function and f(x)=x^(2)+int_(0)^(x) e^(-t) (x-t)dt ,then f)-t) equals to

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)

If int_(0)^(x)f(t)dt = x^(2)-int_(0)^(x^(2))(f(t))/(t)dt then find f(1) .

Let F:[3,5] rarr R be a twice differentiable function on (3,5) such that F(x)= e^(-x) int_(3)^(x) (3t^(2)+2t+4F'(t)) dt . If F'(4)= (alpha e^(beta)-224)/((e^(beta)-4)^(2)) , then alpha+beta is equal to _____

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