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JEE Main20199 Jan 2019Evening ShiftMathematicsArea Under CurvesActual

The area of the region A = x , y : 0 ≤ y ≤ x x + 1 and - 1 ≤ x ≤ 1 in sq. units, is

Options

  1. A4 3
  2. B2
  3. C1 3
  4. D2 3

Correct answer

B. 2

Step-by-step solution

x x = x 2 ,   x ≥ 0 - x 2 ,   x < 0 Area enclosed = ∫ - 1 0 - x 2 + 1 d x + ∫ 0 1 x 2 + 1 d x = - x 3 3 + x - 1 0 + x 3 3 + x 0 1 = 2

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