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MHT CET202310 May 2023Evening ShiftMathematicsArea Under CurvesActual

The area bounded by the X-axis and the curve y=x(x-2)(x+1) is

Options

  1. A37 12 sq. units
  2. B27 12 sq. units
  3. C37 4 sq. units
  4. D27 13 sq. units

Correct answer

A. 37 12 sq. units

Step-by-step solution

array ll & For X-axis, & y=0 & x(x-2)(x+1)=0 & x=0 or x=2 or x=-1 array aligned & Required area = _ -1 ^0 y ~d x+ | ₀^2 y ~d x | & = _ -1 ^0 x(x-2)(x+1) d x+ | ₀^2 x(x-2)(x+1) d x | & = _ -1 ^0 (x^3-x^2-2 x ) d x+ | ₀^2 (x^3-x^2-2 x ) d x | & = [ x^4 4 - x^3 3 -x^2 ]_ -1 ^0+ | [ x^4 4 - x^3 3 -x^2 ]₀^2 | & = 5 12 + |- 8 3 | & = 37 12 sq. units aligned

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