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JEE Main202226 Jul 2022Evening ShiftMathematicsArea Under CurvesActual

The area bounded by the curves y = x 2 - 1 and y = 1 is

Options

  1. A2 3 2 + 1
  2. B4 3 2 - 1
  3. C2 2 - 1
  4. D8 3 2 - 1

Correct answer

D. 8 3 2 - 1

Step-by-step solution

Plotting the diagram of y = x 2 - 1 and y = 1 , we get, Area of the region between the two curves = 2 ∫ 0 2 1 - x 2 - 1 d x = 2 ∫ 0 1 1 + x 2 - 1 d x + ∫ 1 2 1 - x 2 - 1 d x = 2 x 3 3 0 1 + 2 2 x - x 3 3 1 2 = 2 1 3 + 2 2 2 - 2 2 3 - 2 2 - 1 3 = 8 3 2 - 1

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