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NTA Abhyas JEE Main2020MathematicsArea Under CurvesPractice

Let f x = min ⁡ x + 1 , 1 - x   ∀ x ≤ 1 . Then, the area (in sq. units) bounded by y = f x ,   y = 0 and x = 0 from x = 0 to x = 1 is equal to

Options

  1. A1 3
  2. B2 3
  3. C4 9
  4. D1

Correct answer

B. 2 3

Step-by-step solution

f x = x + 1 ; x ≤ 0 1 - x ; x ≥ 0 ∴ Required area is A = ∫ 0 1 1 - x d x = - 2 3 1 - x 3 2 0 1 = - 2 3 0 - 1 = 2 3 sq. units

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