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Example 1
Evaluate where D_{1} is the unit square 0 ≤ x ≤ 1, 0≤ y ≤ 1. The limits of the outside integral are given by 0 ≤ x ≤ 1, and those of the inside integral are given by 0 ≤ y ≤ 1. The iterated integral is thus The inside integral is Then Since D_{1} is a rectangle we may also integrate in the other order, and should get the same answer. The Riemann sums in Section 12.1 were 0.0875, 0.12825.


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