ITERATED INTEGRAL THEOREM

If E is the region

a₁ ≤ x ≤ a₂, b₁(x) ≤ y ≤ b₂(x), c₁(x, y) ≤ z ≤ c₂(x, y),

then

If the region E is a rectangular box

a₁ ≤ x ≤ a₂, b_l ≤ y ≤ b₂, c₁≤ z ≤ c₂,

there are six different iterated integrals over E, corresponding to six different orders of integration. Here they are (in "alphabetical" order).

(1)

(2)

(3)

(4)

(5)

(6)