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NTA Abhyas JEE Main2020MathematicsArea Under CurvesPractice

The area of the smaller part of the circle x 2 + y 2 = 2 cut off by the line x = 1 is

Options

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

Correct answer

B. π 2 - 1 sq. units

Step-by-step solution

x 2 + y 2 = 2 and x = 1 y 2 = 1 ⇒ y = ± 1 Required area = 2 × ∫ 1 2 2 - x 2 d x = 2 x 2 2 - x 2 + s i n - 1 x 2 1 2 = 2 1 2 × 0 + π 2 - 1 2 + π 4 = 2 π 4 - 1 2 = π 2 - 1 sq. units

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