급수와 정적분

$\displaystyle \lim\limits _{n \rightarrow \infty} {\sum\limits _{k = 1} ^{n} f \left( \frac{2 k}{n} \right) \frac{1}{n}} = \frac{1}{2} \int _{0} ^{2} {f \left( x \right) dx}$ $\displaystyle = \frac{1}{2} \int _{0} ^{2} {\left( 6 x ^{2} + x \right) dx}$ $\displaystyle = \frac{1}{2} \left[ 2 x ^{3} + \frac{1}{2} x ^{2} \right] _{0} ^{2} = 9$