Find the area of the region bounded by the curve,

MATHEMATICS · Subjective · AoPS · Mathematics · More Inequalities · More Inequalities

Problem

Find the area of the region bounded by the curve, 2∣x∣+∣y∣+2∣x∣≤12|x| + |y| + \frac{2}{|x|} \le 1, within the square formed by the lines ∣x∣≤12|x| \le \frac{1}{2}, ∣y∣≤12|y| \le \frac{1}{2}.

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