If `|f(x)-f(y)|le2|x-y|^((3)/(2))` `AAx,yinR` and `f(0)=1` then value of `int_(0)^(1)f^2(x)dx` is equal to (a) 1 (b) 2 (c) `sqrt2` (d) 4

abs(f(x)-f(y))le(x-y)^2 forall x,y in R and f(0)=1 then

If 2f(x) - 3 f(1//x) = x," then " int_(1)^(2) f(x) dx is equal to

if int_(0)^(1)f(x)dx=1 and f(2x)=2f(x) then 3int_(1)^(2)f(x)dx is equal to

If f(x)=max{x^(2),(1-x)^(2),(3)/(4)},x in[0,1] then the value of of int_(0)^(1)f(x)dx is

Let f:R rarr R be a continuous function and f(x)=f(2x) is true AA x in R .If f(1)=3 then the value of int_(-1)^(1)f(f(x))dx is equal to (a)6(b) 0 (c) 3f(3)( d) 2f(0)

[ If f(x)=|x|+|x-1|, then int_(0)^(2)f(x)dx equals- [ (A) 3, (B) 2, (C) 0, (D) -1]]

If f(0)=1,f(2)=3,f'(2)=5 and f'(0) is finite,then int_(0)^(1)xf''(2x)dx is equal to (A) zero (B) 1(C)2(D) none of these

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

f(0)=1 , f(2)=e^2 , f'(x)=f'(2-x) , then find the value of int_0^(2)f(x)dx

|f(x)-f(y)|<=2|x-y|^(3/2);f(0)=1, then int_(0)^(1)f^(2)(x)backslash dx