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AP EAMCET202023 Sep 2020Morning ShiftMathematicsArea Under CurvesActual

Calculate the area enclosed by the curves x 2 = 2 - y , x 2 = y

Options

  1. A2 3 square units
  2. B4 3 square units
  3. C8 3 square units
  4. D11 3 square units

Correct answer

C. 8 3 square units

Step-by-step solution

x 2 = 2 - y ,   x 2 = y Intersection point ⇒ 2 - y = y ⇒ y = 1 ⇒ x = ± 1 A = ∫ - 1 1 [ ( 2 - x 2 ) - ( x 2 ) ] d x = 2 ∫ 0 1 ( 2 - 2 x 2 ) d x = 4 x - x 3 3 0 1 = 8 3 square units.

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