NDA 2026 · PYQ · Area between Curves · medium
Consider the curves y = x² and y = 2|x|. What is the area bounded by these curves and the lines x = 0 and x = 1?
Answer
The correct answer is B: 2/3 sq unit. On [0, 1], 2x ≥ x² (since 2x - x² = x(2-x) ≥ 0). Area = ∫₀¹ (2x - x²) dx = [x² - x³/3]₀¹ = 1 - 1/3 = 2/3 sq unit.
- A.1 sq unit
- B.2/3 sq unit✓ Correct
- C.1/2 sq unit
- D.1/3 sq unit
On [0, 1], 2x ≥ x² (since 2x - x² = x(2-x) ≥ 0). Area = ∫₀¹ (2x - x²) dx = [x² - x³/3]₀¹ = 1 - 1/3 = 2/3 sq unit.
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