There are actually many Monte-Carlo techniques for evaluating
integrals, but we will consider only one of the basic ones. The technique least
like standard calculus is sampling - which itself has a number of
variations. Gould and Tobochnik suggest the following gedanken
experiment. You are in a field containing an irregularly shaped pond
and wish to determine the area of the pond using only the material at
hand. You do it by first walking off a box which completely encloses
the lake, and then measuring the lengths of the sides (say in terms of
the natural unit feet) so you know the box's area 
. Now
you grab a bunch of pebbles, throw them randomly up in the air, and
count the number of splashes and the number which land on the ground
within your box. Since the number of pebbles falling into the pond is
proportional to the area of the pond 
, we can determine that
area from the simple ratio
Here 
is the sum of the number of splashes plus the number of
pebbles lying on the ground within the box.
