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NDA 2026 · PYQ · Integral Calculus / Area Between Curves · easy

Consider the curves y = x² and y = 2|x|. What is the area bounded by the curves, the lines x = 0 and x = 1?

  1. A.1 square unit
  2. B.2/3 square unit✓ Correct
  3. C.1/2 square unit
  4. D.1/3 square unit

Explanation

Between x = 0 and x = 1, for x ≥ 0, y = 2x is above y = x² (since at x = 1, 2x = 2 and x² = 1). Area = ∫₀¹ (2x - x²) dx = [x² - x³/3]₀¹ = 1 - 1/3 = 2/3 square units.
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