A
function Φ of the
reals is called a
step function on [a,b]
iff:
For some
finite set of points
a = b
0 < b
1 < ... < b
n = b
Φ is
constant on the
interval (b
i-1 , b
i) for i = 1,2,3, ... , n.
In other words, Φ looks like this:
|
** |**
** |
** **| **
|
----------------------
|
|
|
|
The
integral of a step function is given by:
∫ Φ(x)dx =
Σ (b
i - b
i)c
i