If a differentiable function f(x) satisfies `f(x)=int_(0)^(x)(f(t)cos t-cos(t-x))dt` then value of `(1)/(e)(f''((pi)/(2)))` is

A differentiable function satisfies equation f(x)=int_(0)^(x)(f(t)cos(t)-cos(t-x))dt then (A) f'((pi)/(2))=e (B) lim_(x rarr-oo)f(x)=1 (C) f(x) has minimum value 1-e^(-1) (D) f'(0)=-1

A function f(x) satisfies f(x)=sin x+int_(0)^(x)f'(t)(2sin t-sin^(2)t)dt is

A differentiable function satisfies f(x)=int_(0)^(x){f(t)cost-cos(t-x)}dt. Which is of the following hold good?

Let f(x) be a differentiable function satisfying f(x)=int_(0)^(x)e^((2tx-t^(2)))cos(x-t)dt , then find the value of f''(0) .

If f(x)=int_(0)^(x)e^(-t)f(x-t)dt then the value of f(3) is

If f' is a differentiable function satisfying f(x)=int_(0)^(x)sqrt(1-f^(2)(t))dt+1/2 then the value of f(pi) is equal to

A differentiable function satisfies f(x) = int_(0)^(x) (f(t) cot t - cos(t - x))dt . Which of the following hold(s) good?

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

If f(x) is differentiable function and f(x)=x^(2)+int_(0)^(x) e^(-t) (x-t)dt ,then f)-t) equals to

Let f:R to R be a function which satisfies f(x)=int_(0)^(x) f(t) dt .Then the value of f(In5), is