`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 int_(0)^(x)f(t)dt=x+int_(x)^(1)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 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_(0)^(x)e^(-t)f(x-t)dt then the value of f(3) is

If f(x)=int_(0)^(x)tf(t)dt+2, then

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

If int_(0)^(1) f(t)dt=x^2+int_(0)^(1) t^2f(t)dt , then f'(1/2)is

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 f:R in R is continuous and differentiable function such that int_(-1)^(x) f(t)dt+f'''(3) int_(x)^(1) dt=int_(1)^(x) t^(3)dt-f'(1)int_(0)^(x) t^(2)dt+f'(2) int_(x)^(3) r dt , then the value of f'(4), is