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JEE Main202522 Jan 2025Morning ShiftMathematicsArea Under CurvesActual

The area of the region, inside the circle (x-2 3 )^2+y^2=12 and outside the parabola y^2=2 3 x is :

Options

  1. A3 +8
  2. B6 -16
  3. C3 -8
  4. D6 -8

Correct answer

B. 6 -16

Step-by-step solution

aligned & Required area =2 ₀^ 2 3 ( 4 3 x-x^2 - 2 3 x ) d x & =2 ₀^ 2 3 ( 12-(x-2 3 )^2 - 2 3 x ) d x & =2 [ x-2 3 2 12-(x-2 3 )^2 + 12 2 ⁻¹ ( x-2 3 2 3 ) . & .- 2 3 x^ 3 2 3 2 ]₀^ 2 3 & =2 3 -8 & =6 -16 sq. units. aligned

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