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MHT CET202526 Apr 2025Evening ShiftMathematicsArea Under CurvesActual

If the area bounded by the curve x^2=4 y , X-axis and the line x=4 is divided into equal areas by the line x= , then the value of is ...

Options

  1. A1 32
  2. B32
  3. C(32)^ 1 2
  4. D(32)^ 1 3

Correct answer

D. (32)^ 1 3

Step-by-step solution

The area under the curve x^2 = 4y from x = 0 to x = 4 is found by integrating y = x^2 4 over this interval. A_ total = ₀⁴ x^2 4 dx = 1 4 [ x^3 3 ]₀⁴ = 1 4 64 3 = 16 3 The line x = divides this region into two equal areas, so the area from x = 0 to x = must be 8 3 . ₀^ x^2 4 dx = 8 3 1 4 [ x^3 3 ]₀^ = 8 3 ^3 12 = 8 3 Solving gives ^3 = 32 = 32^ 1/3 , which corresponds to option D .

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