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MHT CET20255 May 2025Evening ShiftMathematicsArea Under CurvesActual

The area of the region bounded by the parabola y^2=27 x and the line x=1 is ______ sq.units.

Options

  1. A2 3
  2. B3 3
  3. C4 3
  4. D7 3

Correct answer

C. 4 3

Step-by-step solution

The parabola y^2 = 27x opens to the right and is symmetric about the x-axis. The region bounded by this parabola and the line x = 1 extends from the vertex at x = 0 to the boundary line. From the parabola equation, y = 3 3 x . By symmetry, we compute the area as twice the area above the x-axis: A = 2 ₀^1 3 3 x dx = 6 3 ₀^1 x^ 1/2 dx A = 6 3 [ 2 3 x^ 3/2 ]₀^1 = 6 3 2 3 = 4 3 The area is 4 3 square units, corresponding to option C.

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