Repeated Integral
A repeated integral is an integral taken multiple times over a single variable (as distinguished from a multiple integral, which
consists of a number of integrals taken with respect to different variables).
The first fundamental theorem of calculus
states that if 
is the integral
of 
, then
 |
(1)
|
Now, if 
, then
 |
(2)
|
It follows by induction that if 
,
then the 
-fold integral of 
is given by
 |  |  |
(3)
|
 |  |  |
(4)
|
Similarly, if 
, then
 |
(5)
|
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double integral