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JEE Main2005MathematicsArea Under CurvesActual

The parabolas y ^2=4 x and x ^2=4 y divide the square region bounded by the lines x =4, y=4 and the coordinate axes. If S₁, S₂, S₃ are respectively the areas of these parts numbered from top to bottom; then S ₁: S ₂: S ₃ is

Options

  1. A1: 2: 1
  2. B1: 2: 3
  3. C2: 1: 2
  4. D1: 1: 1

Correct answer

D. 1: 1: 1

Step-by-step solution

y ^2=4 x and x ^2=4 y are symmetric about line y = x area bounded between y^2=4 x and y=x is ₀^4(2 x -x) d x= 8 3 A _ s ₂ = 16 3 and A _ s ₁ = A _ s ₃ = 16 3 A_ s₁ : A_ s₂ : A_ s₃ :: 1: 1: 1 .

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