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) tf (t) dt , then the value of f(1) is

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.

If f' is a differentiable function satisfying f(x)=int_(0)^(x)sqrt(1-f^(2)(t))dt+1/2 then the value of f(pi) is equal to

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

Iff(x)=x+int_0^1t(x+t)f(t)dt ,t h e nt h ev a l u eof(23)/2f(0) is equal to _________

If int_0^x(f(t))dt=x+int_x^1(t^2.f(t))dt+pi/4-1 , then the value of the integral int_-1^1(f(x))dx is equal to

If f(x)=int_(2)^(x)(dt)/(1+t^(4)) , then

If f'(x)=f(x)+int_(0)^(1)f(x)dx ,given f(0)=1 , then the value of f(log_(e)2) is

"If " f(x)=int(dx)/(x^(1//3)+2) " and "f(0)=12log_(e)2, " then the value of " f(-1) " is"-.