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MHT CET202615 April 2026Morning ShiftMathematicsArea Under CurvesActual

The area of the smaller region bounded by the circle x^2 + y^2 = 4 and the line x = 1 is...

Options

  1. A4 3 - 3
  2. B3 - 3
  3. C4 3 + 3
  4. D3 + 3

Correct answer

A. 4 3 - 3

Step-by-step solution

The equation of the circle is x^2 + y^2 = 4 . The area of the smaller region bounded by the circle and the line x = 1 is given by: A = 2 ₁² 4 - x^2 , dx Using the standard integral formula a^2 - x^2 , dx = x 2 a^2 - x^2 + a^2 2 ⁻¹ ( x a ) , we get: A = 2 [ x 2 4 - x^2 + 2 ⁻¹ ( x 2 ) ]₁² Substituting the limits: A = 2 [ ( 0 + 2 ⁻¹(1) ) - ( 1 2 3 + 2 ⁻¹ ( 1 2 ) ) ] A = 2 [ 2 ( 2 ) - 3 2 - 2 ( 6 ) ] A = 2 [ - 3 2 - 3 ] A = 2 [ 2 3 - 3 2 ] A = 4 3 - 3 Answer: 4 3 - 3

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