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JEE Main20264 April 2026Morning ShiftMathematicsArea Under CurvesActual

The area of the region (x, y): y - |x|, y |x x|, y 0 is:

Options

  1. A1 + ^2 8
  2. B2 + ^2 4
  3. C^2 8 - 1
  4. D4 + ^2 2

Correct answer

B. 2 + ^2 4

Step-by-step solution

The given region is defined by the inequalities y - |x| , y |x x| , and y 0 . Since replacing x with -x leaves the inequalities unchanged, the region is symmetric with respect to the y-axis. We can find the area of the region in the first quadrant ( x 0 ) and multiply it by 2 . For x 0 , the inequalities become: y - x y x x y 0 The condition y 0 and y - x restricts x to the interval [0, ] . In this interval, x 0 , so |x x| = x x . To find the intersection of the curves y = - x and y = x x , we equate them: x x = -

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