By the definition of the definite integral, the value of $\lim _{n \rightarrow \infty}\left[\frac{1^2}{1^3+n^3}+\frac{2^2}{2^3+n^3}+\ldots+\frac{r^2}{r^3+n^3}+\ldots+\frac{1}{2 n}\right]=$