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NTA Abhyas JEE Main2020MathematicsArea Under CurvesPractice

The area (in sq. units) bounded by y = x x and the line y = x is equal to

Options

  1. A1
  2. B2
  3. C1 2
  4. D1 3

Correct answer

D. 1 3

Step-by-step solution

x x = x 2 x ≥ 0 - x 2     x < 0 ∴ Required area = 2 ∫ 0 1 x - x 2 d x = 2 x 2 2 - x 3 3 0 1 = 2 1 2 - 1 3 = 1 3 sq. units

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