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JEE Main2017MathematicsArea Under CurvesActual

The area (in sq. units) of the region x , y : x ≥ 0 , x + y ≤ 3 , x 2 ≤ 4 y a n d y ≤ 1 + x is

Options

  1. A59 12   sq .   units
  2. B3 2   sq .   units
  3. C7 3   sq .   units
  4. D5 2   sq .   units

Correct answer

D. 5 2   sq .   units

Step-by-step solution

Required Area = ∫ 0 1 1 + x d x + ∫ 1 2 3 - x d x - ∫ 0 2 x 2 4 d x = x + 2 3 x 3 2 0 1 + 3 x - x 2 2 1 2 - x 3 12 0 2 = 1 + 2 3 + 4 - 5 2 - 2 3 = 5 2   sq .   units

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