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JEE Main202313 Apr 2023Evening ShiftMathematicsArea Under CurvesActual

The area of the region x , y : x 2 ≤ y ≤ x 2 - 4 , y ≥ 1 is

Options

  1. A4 3 ( 4 2 - 1 )
  2. B4 3 ( 4 2 + 1 )
  3. C3 4 ( 4 2 + 1 )
  4. D3 4 ( 4 2 - 1 )

Correct answer

A. 4 3 ( 4 2 - 1 )

Step-by-step solution

The required diagram is: The shaded region is symmetric about y - axis. Required area = 2 ∫ 1 2 y d y + ∫ 2 4 4 - y d y = 2 y 3 / 2 3 2 1 2 - 2 ( 4 - y ) 3 / 2 3 2 4 = 4 3 ( 4 2 - 1 ) Hence this is the correct option.

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