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Example 2
Evaluate where D_{2} is the region in Figure 12.2.2: 0 ≤ x ≤ 1, x^{2} ≤ y ≤ √x. The limits on the outside integral are given by 0 ≤ x ≤ 1, and those on the inside integral by x^{2} ≤ y ≤ √x, so the iterated integral is Figure 12.2.2 The Riemann sums in Section 12.1 were 0.05375, 0.04881. In many applications the region D is given verbally, and part of the problem is to find inequalities which describe D.


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