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MHT CET202519 Apr 2025Morning ShiftMathematicsArea Under CurvesActual

The ratio of the areas bounded by the curves y = x and y = 2 x between x=0, x= 3 and X -axis is

Options

  1. A2 : 1
  2. B1: 1
  3. C2: 1
  4. D1: 3

Correct answer

C. 2: 1

Step-by-step solution

The ratio of areas bounded by y = x and y = 2x from x = 0 to x = 3 is determined by evaluating the respective definite integrals. The area under y = x evaluates to A₁ = ₀^ /3 x , dx = x |₀^ /3 = 3 2 - 0 = 3 2 . For y = 2x , the area is A₂ = ₀^ /3 2x , dx = 1 2 2x |₀^ /3 = 1 2 3 2 - 0 = 3 4 . The ratio A₁ : A₂ = 3 2 : 3 4 = 2 : 1 , which corresponds to option C . The final answer is C .

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