Let `f(x)-|x-1|+|x-2|`. `I = int_(0)^(1)f(x)dx` , `M -` the minimum value of `f`, `N=f'(x)` for `x < - 4`and `C-` the value of `f''(4)` .Then the value of `(M^(2)-N^(2)-IC)/(2)` is :

Let f(x)=|x-1|+|x-2|,I=int_(0)^(3)f(x)dx , M = the minimum value of f . N=f'(x) for xlt-4 and c= the value of f'(4) .Then the value of (M^(2)-N^(2)-IC)/(2) 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 ,given f(0)=1 , then the value of f(log_(e)2) is

Let f(x) be a continuous and periodic function such that f(x)=f(x+T) for all xepsilonR,Tgt0 .If int_(-2T)^(a+5T)f(x)dx=19(ag0) and int_(0)^(T)f(x)dx=2 , then find the value of int_(0)^(a)f(x)dx .

Let f : R to R be continuous function such that f (x) + f (x+1) = 2, for all x in R. If I _(1) int_(0) ^(8) f (x) dx and I _(2) = int _(-1) ^(3) f (x) dx, then the value of I _(2) +2 I _(2) is equal to "________"

If f(x)+f(2-x)=0 , then int_(0)^(2)(1)/(1+2^(f(x)))dx=