Let function `f:R rarr R` satisfying the equation `f(x)=(1+x^(2))(1+int_(0)^(x)(f^(2)(t))/(1+t^(2))dt)` ,then absolute value of `f(1)`

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

Let f(x) be a continuous function defined from [0,2]rarr R and satisfying the equation int_(0)^(2)f(x)(x-f(x))dx=(2)/(3) then the value of 2f(1)

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

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

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

A continuous function f: R rarrR satisfies the equation f(x)=x+int_(0)^(1) f(t)dt. Which of the following options is true ?

A derivable function f(x) satisfies the relation f(x)=int_(0)^(1)xf(t)dt+int_(0)^(x)x^(2)f(t)dt. The value of (2f'(1))/(f(1)) is