The Gini index given by $2{\displaystyle \underset{0}{\overset{1}{}}}(x-f(x))dx,$ is a measure of a country's income equality on a scale of $0($perfectly equal$)$ to $1($perfectly unequal$).$ If a country has $f(x)=x^{1\mathrm{.}7},$ find the value of their Gini Index.

$2(\frac{1}{2}-\frac{1}{\mathrm{.}7})$

$(\frac{1}{2}-\frac{1}{1\mathrm{.}7})$

$(\frac{1}{2}-\frac{1}{\mathrm{.}7})$

$2(\frac{1}{2}-\frac{1}{2\mathrm{.}7})$

$2(\frac{1}{2}-\frac{1}{1\mathrm{.}7})$