Let `f` be a continuous function on `(0,oo)` and satisfying `f(x)=(log_(e)x)^(2)-int_(1)^(e)(f(t))/(t)dt` for all `x>=1,` then `f(e)` equals

Let f be a continuous function on R and satisfies f(x)=e^(x)+int_(0)^(1)e^(x)f(t)dt, then which of the following is(are) correct?

A continuous function f(x) satisfies the relation f(x)=e^(x)+int_(0)^(1)e^(x)f(t)dt then f(1)=

f(x) = int_(x)^(x^(2))(e^(t))/(t)dt , then f'(t) is equal to :

If f(x)=int_(log_(e)x)^(x)(dt)/(x+t) then f'(x)=

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) .

If a function y=f(x) such that f'(x) is continuous function and satisfies (f(x))^(2)=k+int_(0)^(x) [{f(t)}^(2)+{f'(t)}^(2)]dt,k in R^(+) , 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…………………..

A Function f(x) satisfies the relation f(x)=e^(x)+int_(0)^(1)e^(x)f(t)dt* Then (a)f(0) 0