Let the function f be defined by
`f (x) = |x-1| -1/2, 0 le x le 2, f (x +2 ) = f (x)` for all `x in R.`
Evaluate `(i) int _(0) ^(100) f (x) dx`
(ii) ` int _(0) ^(1)| f(2x ) |dx`

If f(a-x)=f(x) and int_(0)^(a//2)f(x)dx=p , then : int_(0)^(a)f(x)dx=

Let a function f:R to R be defined as f (x) =x+ sin x. The value of int _(0) ^(2pi)f ^(-1)(x) dx will be:

Let a function f:R to R be defined as f (x) =x+ sin x. The value of int _(0) ^(2pi)f ^(-1)(x) dx will be:

If f(x)=x(x-1), 0 le x le 1, and f(x+1)=f(x) AA x in R , then |int_(2)^(4)f(x)dx| is _____________

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)=|x-1| then int_(0)^(2)f(x)dx is

if f(x)=|x-1| then int_(0)^(2)f(x)dx is

if f(x) = {[3x+4 , 0 le x le 2],[5x , 2 le x le 3]}, then evaluate int_(0)^(3) f(x) dx.

f(x) = {(1-2x", for " x le0),(1+2x", for "xgt0):} then int_(-1) ^(1) f(x) dx=

The function f(x) is defined in 0 le x le1, find the domain of definition of f(2x-1)