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JEE Main2014MathematicsArea Under CurvesActual

The area (in sq. unit) of the region described by A = x , y : x 2 + y 2 ≤ 1 and y 2 ≤ 1 - x is

Options

  1. Aπ 2 - 2 3
  2. Bπ 2 + 2 3
  3. Cπ 2 + 4 3
  4. Dπ 2 - 4 3

Correct answer

C. π 2 + 4 3

Step-by-step solution

Area of shaded region = area of semicircle + area of region B C A = π 2 + 2 ∫ 0 1 1 - x · d x = π 2 + 2 - 2 3 1 - x 3 / 2 0 1 = π 2 - 4 3 - 1 = π 2 + 4 3 sq. unit

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