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JEE Main202127 Jul 2021Evening ShiftMathematicsArea Under CurvesActual

The area of the region bounded by y - x = 2 and x 2 = y is equal to :-

Options

  1. A16 3
  2. B2 3
  3. C9 2
  4. D4 3

Correct answer

C. 9 2

Step-by-step solution

y - x = 2 , x 2 = y Now, x 2 = 2 + x ⇒ x 2 - x - 2 = 0 ⇒ x + 1 x - 2 = 0 ⇒ x = - 1 , 2 Required area = ∫ - 1 2 2 + x - x 2 d x = 2 x + x 2 2 - x 3 3 - 1 2 = 4 + 2 - 8 3 - - 2 + 1 2 + 1 3 = 6 - 3 + 2 - 1 2 = 9 2 square units

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