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JEE Main202225 Jul 2022Morning ShiftMathematicsArea Under CurvesActual

The area of the region given by A = x , y : x 2 ≤ y ≤ min x + 2 , 4 - 3 x is

Options

  1. A31 8
  2. B17 6
  3. C19 6
  4. D27 8

Correct answer

B. 17 6

Step-by-step solution

The graph of y = x 2   &   y = min x + 2 , 4 - 3 x will be From the graph, required area A = ∫ - 1 1 2 x + 2 - x 2 d x + ∫ 1 2 1 4 - 3 x - x 2 d x = x 2 2 + 2 x - x 3 3 - 1 1 2 + 4 x - 3 x 2 2 - x 3 3 1 2 1 = 17 6

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