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How To Solve Multiple Integral Problems
Multiple integration problems can be solved by a threestep process as shown in Examples 3 and 4.
We can also integrate over a region in the (y, x) plane instead of the (x, y) plane. A region D in the (y, x) plane has the form b_{1} ≤ y ≤ b_{2}, a_{1 }(y) ≤ x ≤ a_{2}(y), as shown in Figure 12.2.5. The double integral over D is equal to the iterated integral with dy on the outside and dx inside, Figure 12.2.5 Some regions, such as rectangles and ellipses, may be regarded as regions in either the (x, y) plane or the (y, x) plane (Figure 12.2.6). (a) D as an (x, y) Region (b)D as a (y, x) Region Figure 12.2.6


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