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JEE Main202226 Jun 2022Evening ShiftMathematicsArea Under CurvesActual

The area of the region bounded by y 2 = 8 x and y 2 = 16 3 - x is equal to

Options

  1. A32 3
  2. B40 3
  3. C16
  4. D9

Correct answer

C. 16

Step-by-step solution

Given curves are y 2 = 8 x and y 2 = 16 3 - x ⇒ 8 x = 48 - 16 x ⇒ x = 2 , so y = ± 4 Required area = 2 ∫ 0 4 3 - y 2 16 - y 2 8 d y = 2 3 y - y 3 48 - y 3 24 0 4 = 2 12 - 64 48 - 64 24 = 16

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