In economics, the Gini index of inequality (G), is one of the ways to measure the degree of concentration in the distribution of resources among members of a population. Is given by:

$$G = 2\int\limits_{0}^{1}[x-L(x)]dx$$

The L (x) function is called Lorentz curve and Gini index (G) always has a value between 0 and 1, so that the smaller the index, the more uniform the distribution of income, and the higher the index , will be the most concentrated income in the hands of a few individuals. If, for a given population, the Lorentz curve is L(x) = 0,8^2+0,2x, calculate the Gini index.

Question

In economics, the Gini index of inequality (G), is one of the ways to measure the degree of concentration in the distribution of resources among members of a population. Is given by: 

$$G = 2\int\limits_{0}^{1}[x-L(x)]dx$$

The L (x) function is called Lorentz curve and Gini index (G) always has a value between 0 and 1, so that the smaller the index, the more uniform the distribution of income, and the higher the index , will be the most concentrated income in the hands of a few individuals. If, for a given population, the Lorentz curve is L(x) = 0,8^2+0,2x, calculate the Gini index.