Consider a function `f: [0, 1] -> R` satisfying `int_0 ^1 (f(x)(x-f(x))dx = 1/12`, then, `f'(1)` is `k` where `[1/k]` is

Function f satisfies the relation f(x)+2f((1)/(1-x))=x AA x in R-{1,0} then f(2) is equal to

There exists a function f(x) satisfying 'f (0)=1,f(0)=-1,f(x) lt 0,AAx and

A continuous function f(x) satisfies the relation f(x)=e^x+int_0^1 e^xf(t)dt then f(1)=

A continuous function f(x) satisfies the relation f(x)=e^x+int_0^1 e^xf(t)dt then f(1)=

A continuous function f(x) satisfies the relation f(x)=e^(x)+int_(0)^(1)e^(x)f(t)dt then f(1)=

A continuous real function f satisfies f(2x)=3(f(x)) AA x in R . If int_0^1 f(x)dx=1, then find the value of int_1^2f(x)dx .

If a continuous function f on [0, a] satisfies f(x)f(a-x)=1, a >0, then find the value of int_0^a(dx)/(1+f(x))