According to Figure 7.1.6(a), the top half of the inner loop of this limaçon is traced for . The full inner loop is traced for , or equivalently, . (Indeed, this is the hardest part of the calculation, determining the range of for which the inner loop is drawn.) Of course, the area of the top half of the inner loop could be computed and doubled to get the area of the full inner loop.
Applying the appropriate formula from Table 7.2.1, the area is computed as follows.
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