`f(x)=(sinx-xcosx)/(x^2)` if `x !=0` and f(0)=0 then `int_0^1 f(x) dx` is

Consider the function defined on [0,1] rarr R , f(x) =(sinx- xcosx)/(x^(2)), if x ne 0 and f(0) =0 int _(0)^(1)f(x) is equal to

Consider the function defined on [0,1] rarr R , f(x) =(sinx- xcosx)/(x^(2)), if x ne 0 and f(0) =0 int _(0)^(1)f(x) is equal to

if f(x)=|x-1| then int_(0)^(2)f(x)dx is

if f(x)=|x-1| then int_(0)^(2)f(x)dx is

If f'(x) = f(x)+ int _(0)^(1)f (x) dx and given f (0) =1, then int f (x) dx is equal to :

If f'(x) = f(x)+ int _(0)^(1)f (x) dx and given f (0) =1, then int f (x) dx is equal to :

If f(0)=2, f'(x) =f(x), phi (x) = x+f(x) then int_(0)^(1) f(x) phi (x) dx is

If int_0^1 f(x) dx = 1, int_0^1 xf(x) dx = a, int_0^1 x^2 f(x) dx = a^2 , then int_0^1 (a - x)^2 f(x) dx is equal to :

If f(x)+int{f(x)}^(-2)dx=0 and f(1)=0 then f(x) is

If f(x) and g(x) be continuous functions in [0,a] such that f(x)=f(a-x),g(x)+g(a-x)=2 and int_0^a f(x)dx=k , then int_0^a f(x)g(x)dx= (A) 0 (B) k (C) 2k (D) none of these