If `f(x)=1+1/x int_1^x f(t) dt,` then the value of `(e^-1)` is

If int_(0)^(x) f(t)dt=x+int_(x)^(1) t f(t) dt , then the value of f(1), is

If int_(0) ^(x) f (t) dt = x + int _(x ) ^(1) t f (t) dt, then the value of f (1) , is

If f(x)=int_(1)^(x)(ln t)/(1+t)dt, then

If f(x)=int_(0)^(x)e^(-t)f(x-t)dt then the value of f(3) is

If f(x) = int_1^x lnt/(1+t) dt where x>0 then the values of x satisfying the equation f(x)+f(1/x) = 2 are (i)2 (ii)e (iii)e^(-2) (iv)e^(2)

If f(x)=x+int_(0)^(1)t(x+t)f(t)dt, then the value of (23)/(2)f(0) is equal to

If int_(0)^(x)f(t)dt=x+int_(x)^(1)f(t)dt ,then the value of f(1) is

f(x)=int_(0)^( pi)f(t)dt=x+int_(x)^(1)tf(t)dt, then the value of f(1) is (1)/(2)

If f(x)=x+int_(0)^(1)t(x+t)f(t)dt, then find the value of the definite integral int_(0)^(1)f(x)dx