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AP EAMCET202419 May 2024Evening ShiftMathematicsArea Under CurvesActual

The area (in sq. units) of the smaller region lying above the X-axis and bounded between the circle x^2+y^2=2 a x and the parabola y^2=a x is

Options

  1. A2 a^2 ( 4 - 2 3 )
  2. Ba^2 ( 4 - 2 3 )
  3. Ca^2 ( 4 + 2 3 )
  4. Da^2 ( ^2 4 - 1 3 )

Correct answer

B. a^2 ( 4 - 2 3 )

Step-by-step solution

Given the curve x^2+y^2=2 a x (x-a)^2+y^2=a^2 and, y^2=a x Since, area of shaded part = a^2 4 - ₀^a a x d x aligned & = a^2 4 - a ₀^a x d x= a^2 4 - a ( x^ 3 / 2 3 2 )₀^a & = a^2 4 - 2 a^2 3 =a^2 ( 4 - 2 3 ) sq. units. aligned

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