Given $\displaystyle {L}_{{n}}=$ $\displaystyle \frac{{1}}{{n}}{\sum_{{{i}={1}}}^{{n}}}{\left[{\left({7}+{\left({i}-{1}\right)}\frac{{1}}{{n}}\right)}^{{7}}{\cos{{\left({7}+{\left({i}-{1}\right)}\frac{{1}}{{n}}\right)}}}\right]}$, express the limit as $\displaystyle {n}\to\infty$  as a definite integral, that is provide $\displaystyle {a}$, $\displaystyle {b}$ and $\displaystyle {f{{\left({x}\right)}}}$ in the expression $\displaystyle {\int_{{{a}}}^{{b}}}{f{{\left({x}\right)}}}{\left.{d}{x}\right.}$. 

$\displaystyle {a}=$ , $\displaystyle {b}=$ , $\displaystyle {f{{\left({x}\right)}}}=$ Preview Question 6 Part 3 of 3