Let `f(x)=|x-2|` and `g(x)=f(f(x))`,`x in[0,4]` .Then `int_(0)^(3)(g(x)-f(x))dx` is equal to

Let f and g be continuous fuctions on [0, a] such that f(x)=f(a-x)" and "g(x)+g(a-x)=4 " then " int_(0)^(a)f(x)g(x)dx is equal to

Let f(x)=f(a-x) and g(x)+g(a-x)=4 then int_0^af(x)g(x)dx is equal to (A) 2int_0^af(x)dx (B) int_0^af(x)dx (C) 4int_0^af(x)dx (D) 0

If f(x)=|x-2|" and "g(x)=f(f(x)), then for 2ltxlt4,g'(x) equals

The value of int [f(x)g''(x) - f''(x)g(x)] dx is equal to

If f(x) =(x-1)/(x+1),f^(2)(x)=f(f(x)),……..,……..f^(k+1)(x)=f(f^(k)(x)) ,k=1,2,3,……and g(x)=f^(1998)(x) then int_(1//e)^(1) g(x)dx is equal to

If f(x)=|x-1|" and "g(x)=f(f(f(x))) , then for xgt2,g'(x) is equal to

Let a gt 0 and f(x) is monotonic increase such that f(0)=0 and f(a)=b, "then " int_(0)^(a) f(x) dx +int_(0)^(b) f^(-1) (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

I=int_(0)^(2)(e^(f(x)))/(e^(f(x))+e^(f(2-x)))dx is equal to

If f and g are continuous functions on [ 0, pi] satisfying f(x) +f(pi-x) =1=g (x)+g(pi-x) then int_(0)^(pi) [f(x)+g(x)] dx is equal to