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
- A37 12 sq. units
- B27 12 sq. units
- C37 4 sq. units
- 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