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)
|