If the area of bounded between the x-axis and the graph of `y=6x-3x^2` between the ordinates `x=1a n dx=a` is `19` units, then `a` can take the value `4or-2` two value are in (2,3) and one in `(-1,0)` two value are in (3,4) and one in `(-2,-1)` none of these

Options

A. one value in (2, 3)
B. one value in `(-2, -1)`
C. one value in `(-1,0)`
D. one value in `(3,4)`

Answer

B, D

Explanation

`I=int(6x-3x^(2))dx=(6x^(2))/(2)-(3x^(3))/(3)=3x^(2)-x^(3)=x^(2)(3-x)`

`A_(1)=I(2)-I(3)=4-2=2" units"`
`A_(2)=I(2)-I(3)=4-0=4" units"`
`A_(3)=I(3)-I(4)=0-(-16)=16" units"`
`rArr" one value of a will lie in "(3, 4)`.
Using symmetry, order will lie i `(-2,-1)`