Find the area of the region bounded by the curve `y=x^(3),y=x+6" and "x=0`

Answer

N/a

Explanation

We have , `y=x^(3),y=x+6" and "x=0`

`:. X^(3)=x+6`
`rArrx^(3)-x=6`
`rArrx^(3)-x-6=0`
`rArrx^(2)(x-2)+2x(x-2)+3(x-2)=0`
`rArr(x-2)(x^(2)+2x+3)=0`
`rArrx=2," with two imaginary point"`
`:." Required area of shaded region "=int_(0)^(2)(x+6-x^(3))dx`
`=[(x^(2))/2+6x-(x^(4))/4]_(0)^(2)`
`=[4/2+12-16/4-0]`
`=[2+12-4]=10" sq units"`