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JEE Main202324 Jan 2023Morning ShiftMathematicsArea Under CurvesActual

The area enclosed between the curves y 2 + 4 x = 4 and y - 2 x = 2 is

Options

  1. A25 3
  2. B22 3
  3. C9
  4. D23 3

Correct answer

C. 9

Step-by-step solution

Given: y 2 = - 4 x + 4 y = 2 x + 2 Required area = ∫ - 4 2 4 - y 2 4 - y - 2 2 d y = ∫ - 4 2 2 - y 2 4 - y 2 d y = 2 y - y 3 12 - y 2 4 - 4 2 = 4 - 8 12 - 1 - - 8 + 64 12 - 16 4 = 15 - 6 = 9 sq. units

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