If the area bounded by the curve `f(x)=x^(1/3)(x-1)` and the x-axis is `A ,` then the value of `28 A` is____

Answer

9

Explanation

Graph of f(x) is as

`A=overset(1)underset(0)int(x^(4//3)-x^(1//3))dx=(3)/(7)x^(3//7)-(3)/(4)x^(4//3)]_(0)^(1)`
`=|(3)/(7)-(3)/(4)|=3|(4-7)/(28)|=(9)/(28)`
`"or "28A=9`