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JEE Main20253 Apr 2025Evening ShiftMathematicsArea Under CurvesActual

The area of the region (x, y):|x-y| y 4 x is

Options

  1. A512
  2. B1024 3
  3. C512 3
  4. D2048 3

Correct answer

B. 1024 3

Step-by-step solution

aligned & |x-y| y 4 x & Now y=|x-y| & y^2=(x-y)^2 & y= x 2 and x=0 aligned aligned & Now area = ₀⁶⁴ (4 x - x 2 ) dx & = [ 4 x ^ 3 / 2 3 / 2 - x ^2 4 ]₀⁶⁴= 8 3 8^3- 64^2 4 =64^2 ( 1 12 ) & = 1024 3 aligned

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