csat-suneung· South-Korea· csat__math-science3 marks
For the function $f ( x ) = x ^ { 3 } + x$, find the value of $\lim _ { n \rightarrow \infty } \frac { 1 } { n } \sum _ { k = 1 } ^ { n } f \left( 1 + \frac { 2 k } { n } \right)$. [3 points]
For the function $f ( x ) = x ^ { 3 } + x$, find the value of $\lim _ { n \rightarrow \infty } \frac { 1 } { n } \sum _ { k = 1 } ^ { n } f \left( 1 + \frac { 2 k } { n } \right)$. [3 points]