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Iterated Integral Theorem
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, bl ≤ 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) The Iterated Integral Theorem shows that each of these iterated integrals is equal to the triple integral
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