The area of the region bounded by y = min{|x|, 1} and y = max{|x|, 1} for |x| ≤ 2 is:
The area of the region bounded by y = min{|x|, 1} and y = max{|x|, 1} for |x| ≤ 2 is:
- A. 2 sq units
- B. 3 sq units
- C. 4 sq units
- D. 1 sq unit
Answer: A) 2 sq units
Explanation: For |x|≤1, y from |x| to 1. For 1≤|x|≤2, y from 1 to |x|. Area = 2[∫[0 to 1] (1 − x) dx + ∫[1 to 2] (x − 1) dx] = 2[(1−1/2) + (2−2 − (1/2−1))] = 2[1/2 + 1/2] = 2 sq units.
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