The area bounded by y = 2 − |2 − x| and the x-axis is:
The area bounded by y = 2 − |2 − x| and the x-axis is:
- A. 4 sq units
- B. 2 sq units
- C. 6 sq units
- D. 8 sq units
Answer: A) 4 sq units
Explanation: y = 2 − |2 − x|. For x ≤ 2: y = 2 − (2 − x) = x. For x ≥ 2: y = 2 − (x − 2) = 4 − x. Area = ∫[0 to 2] x dx + ∫[2 to 4] (4 − x) dx = [x²/2]₀² + [4x − x²/2]₂⁴ = 2 + (16 − 8) − (8 − 2) = 2 + 8 − 6 = 4 sq units.
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