$[7pts]$

Assume $\{x_0,x_1,$dots,$x_n\}is$ a regular partition $of$ the interval $[a,b]=[1,27]$ with

$x=\frac{b-a}{n}.$

$(a)$ Convert the $limit\underset{n}{lim}{\displaystyle \underset{i=1}{\overset{n}{}}}\frac{\sqrt[\phantom{2}]{c_i^{\frac{2}{3}}+1}}{c_i^{\frac{1}{3}}}x$ into a definite integral

$(b)$ Show all work needed $to$ evaluate the integral manually, including any change $of$ boundaries. Round

your answer $to2$ decimal places.