Find the area bounded by the curve `y=(x-1)(x-2)(x-3)` lying between the ordinates `x=0a n dx=3.`

Explanation

curve is given by, `y=(x-1)(x-2)(x-3)`
It is lying between the ordinates `x=0` a n d `x=3.`
from given , required area is ,
`int_0^3(x-1)(x-2)(x-3)dx`
`=int_0^3(x^3-6x^2+11x-6)dx`
`=[x^4/4]_0^3-6[x^3/3]_0^3+11[x^2/2]_0^3-[6x]_0^3`
`=81/4-54+99/2-18`
`=-9/4`
area can not be negative, sp area`=9/4` sq.units.