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MHT CET202619 April 2026Evening ShiftMathematicsArea Under CurvesActual

The area (in sq. units) of the region bounded by the curve y = 2x - x^2 and the X-axis is...

Options

  1. A4 3
  2. B8 3
  3. C20 3
  4. D2 3

Correct answer

A. 4 3

Step-by-step solution

The given curve is y = 2x - x^2 . To find the points of intersection with the X-axis, set y = 0 : 2x - x^2 = 0 x(2 - x) = 0 x = 0, x = 2 The required area is the integral of the curve from x = 0 to x = 2 : A = ₀² (2x - x^2) dx A = [ x^2 - x^3 3 ]₀² A = ( 2^2 - 2^3 3 ) - 0 A = 4 - 8 3 = 4 3 sq. units. Answer: 4 3

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