The rectangle rule, also called the rectangle method, is a numerical integration rule which approximates an integral
by areas of rectangles. For
a partition 
with equal width 
,
the composite left, right, and midpoint rules are
 |  |  |
(1)
|
 |  |  |
(2)
|
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(3)
|
The midpoint rule is generally the most accurate of the three. If 
is a continuous function
with a continuous second derivative,
its error satisfies
 |
(4)
|
