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JEE Main202227 Jul 2022Evening ShiftMathematicsArea Under CurvesActual

The area of the region enclosed by y ≤ 4 x 2 , x 2 ≤ 9 y and y ≤ 4 , is equal to

Options

  1. A40 3
  2. B56 3
  3. C112 3
  4. D80 3

Correct answer

D. 80 3

Step-by-step solution

Plotting the required region Enclosed area = 2 ∫ 0 4 3 y - y 2 d y = 2 ∫ 0 4 5 y 2 d y = 5 2 3 y 3 2 0 4 = 10 3 ( 4 ) 3 2 = 80 3

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