Find a function f, continous for all x(and not zero everywhere) such that `f^(2)(x)=int_(0)^(x)(f(t) sin t)/(2+ cost)dt`

A function f is continuous for all x (and not everywhere zero) such that f^(2)(x)=int_(0)^(x)f(t)(cost)/(2+sint)dt . Then f(x) is

A function f is continuous for all x (and not everywhere zero) such that f^(2)(x)=int_(0)^(x)f(t)(cost)/(2+sint)dt . Then f(x) is

For the function f(x)=int_(0)^(x)(sin t)/(t)dt where x>0

Given a function g, continous everywhere such that g (1)=5 and int _(0)^(1) g (t) dt =2. If f (x) =1/2 int _(0) ^(x) (x -t)^(2) g (t) dt, then find the value of f '(1)+f''(1).

Given a funtion g, continous everywhere such that g (1)=5 and int _(0)^(1) g (t) dt =2. If f (x) =1/2 int _(0) ^(x) (x -t)^(2) g (t) dt, then find the value of f ''(1)+f''(1).

Let f(x) be a continuous function for all x, which is not identically zero such that {f(x)}^(2)=int_(0)^(x)f(t)(2sec^(2)t)/(4+tan t)dt and f(0)=ln4

If f(-x)+f(x)=0 then int_(a)^(x)f(t)dt is

Given a function 'g' continous everywhere such that int _(0) ^(1) g (t ) dt =2 and g (1)=5. If f (x ) =1/2 int _(0) ^(x) (x-t) ^(2)g (t)dt, then the vlaue of f'''(1)-f''(1) is:

Given a function 'g' continous everywhere such that int _(0) ^(1) g (t ) dt =2 and g (1)=5. If f (x ) =1/2 int _(0) ^(x) (x-t) ^(2)g (t)dt, then the vlaue of f'(1)-f'(1) is: