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NTA Abhyas JEE Main2020MathematicsArea Under CurvesPractice

The area (in sq. units) bounded by x + y = 2 in the first and third quadrant is (where, . is the greatest integer function),

Options

  1. A4
  2. B3
  3. C6
  4. D10

Correct answer

C. 6

Step-by-step solution

x + y = 2 (Let x , y ≥ 0 ) ⇒ x , y = 2 , 0 or 1 , 1 or 0 , 2 If x = 2 and y = 0 ⇒ x ∈ 2 , 3 and y ∈ 0 , 1 and so on Since, the curve is symmetric in the I s t and I I I r d quadrant Hence, the required area = 6 1 × 1 = 6 sq. units

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