If `f` be decreasing continuous function satisfying `f(x + y) = f(x) + f(y)-f(x) f(y) Y x, y epsilon R ,f'(0)=1` then `int_0^1 f(x)dx` is

If f be decreasing continuous function satisfying f(x+y)=f(x)+f(y)-f(x)f(y)Yx,y varepsilon R,f'(0)=1 then int_(0)^(1)f(x)dx is

Let f be a continuous function satisfying f(x + y) = f (x) f( y) (x, y in R) with f(1) = e then the value of int(xf(x))/(sqrt(1+f(x)))dx is

IF f(x+f(y))=f(x)+y AA x, y in R and f(0)=1 , then int_(0)^(10)f(10-x)dx is equal to

A function f(x) satisfies the relation f(x+y) = f(x) + f(y) + xy(x+y), AA x, y in R . If f'(0) = - 1, then

Let f be differentiable function satisfying f((x)/(y))=f(x) - f(y)"for all" x, y gt 0 . If f'(1) = 1, then f(x) is