If `S` is the sum of cubes of possible value of `c` for which the area of the figure bounded by the curve `y=8x^2-x^5,` then straight lines `x=1a n dx=c` and the abscissa axis is equal to `(16)/3,` then the value of `[S],w h e r e[dot]` denotest the greatest integer function, is____

Answer

2

Explanation

`"Given that "overset(c)underset(1)intydx =(16)/(3)`
`rArr" "overset(c)underset(1)int(8x^(2)-x^(5))dx=(16)/(3)c=(8-sqrt(17))^(1//3)" "(cgt0)`
`"Area "OFE =overset(c)underset(0)int(8x^(2)-x^(5))dx=(8)/(3)" "(Cgt0)`
`"so "c=-1`
`"Hence, "c=-1 and (8-sqrt(17))^(1//3)`