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JEE Main202228 Jun 2022Morning ShiftMathematicsArea Under CurvesActual

The area of the region S = x , y : y 2 ≤ 8 x , y ≥ 2 x , x ≥ 1 is

Options

  1. A5 2 6
  2. B19 2 6
  3. C13 2 6
  4. D11 2 6

Correct answer

D. 11 2 6

Step-by-step solution

Plotting the region for the given inequalities y 2 ≤ 8 x ,   y ≥ 2 x ,   x ≤ 1 , we get Required area will be ∫ 1 4 2 2 x - 2 x d x = 2 2 x 3 2 3 / 2 1 4 - 2 x 2 2 1 4 = 4 2 3 8 - 1 - 2 3 16 - 1 = 28 2 3 - 15 2 2 = 11 2 6

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