We would like to evaluate the following definite integral,
where we assume that 
is real-valued on 
.
Figure 9
depicts a typical integral to be evaluated.
Figure 9: Monte Carlo Integration.
The idea is to manipulate the definite integral into a form that can be solved
by Monte Carlo. To do this, we define the following function on 
,
and insert into Eq. (64) to obtain the following expression for the integral I:
Note that 
can be viewed as a uniform pdf on the interval 
, as
depicted in
Figure 9.
Given that 
is a pdf, we observe that the integral on the right
hand side of Eq. (66) is simply the expectation value for 
:
Figure 10: Uniform pdf on [a,b].
![Uniform pdf on [a,b].](../GIFFIGS/MCF10.GIF){kind=link}