If `f(1/x)+x^2f(x)=0, xgt0` and `a=int_(1/x)^x f(t)dt, 1/2lexle2`, then `a=`
(A) `1` (B) `0` (C) `f(2)-f(1/2)` (D) none of these

If f((1)/(x)) +x^(2)f(x) =0, x gt0 and I= int_(1//x)^(x) f(t)dt, (1)/(2) le x le 2x , then I is equal to

If intf(x)*cosxdx=1/2{f(x)}^2+c , then f(0)= (A) 1 (B) 0 (C) -1 (D) none of these

If f(x)=1+1/x int_1^x f(t)dt , then the value of f(e^(-1)) is (a) 1 (b) 0 (c) -1 (d) none of these

Let f(x)=max. {2-x,2,1+x} then int_(-1)^1 f(x)dx= (A) 0 (B) 2 (C) 9/2 (D) none of these

If f(x)=int_(0)^(x)|t-1|dt , where 0lexle2 , then

If f(x)=x^(2)int_(0)^(1)f(t)dt+2 , then

If f(x) is a differentiable real valued function such that f(0)=0 and f\'(x)+2f(x) le 1 , then (A) f(x) gt 1/2 (B) f(x) ge 0 (C) f(x) le 1/2 (D) none of these

f(x)=int_0^x f(t) dt=x+int_x^1 tf(t)dt, then the value of f(1) is

Let f(x) be a continuous function such that f(a-x)+f(x)=0 for all x in [0,a] . Then int_0^a dx/(1+e^(f(x)))= (A) a (B) a/2 (C) 1/2f(a) (D) none of these

If int_(0) ^(x) f (t) dt = x + int _(x ) ^(1) t f (t) dt, then the value of f (1) , is