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(x)=int_0^x (sint)/(t)dt,xgt0, then

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

Suppose f is continuous, f(0)=0,f(1)=1,f^(prime)(x)>0"and"int_0^1f(x)dx=1/3, Find the value of the definite integral int_0^1f^-1(y)dy.

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

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

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

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