If a function f is such that `f(x)=int_0^x dx/(f(x)) and f(1)=sqrt2,` then the value of `f(2)` is

If f(x)=int(dx)/((1+x^2)^ (3/2) and f(0)=0 then what is the value of f(1)?

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

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) is a continuous function in [0,pi] such that f(0)=f(x)=0, then the value of int_(0)^(pi//2) {f(2x)-f''(2x)}sin x cos x dx is equal to

If f(x) is a continuous function in [0,pi] such that f(0)=f(x)=0, then the value of int_(0)^(pi//2) {f(2x)-f''(2x)}sin x cos x dx is equal to

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

Let f(x) be a differentiable function such that f(x)=x^2 +int_0^x e^-t f(x-t) dt then int_0^1 f(x) dx=