Write the limit $\underset{|k|}{lim}=0{\displaystyle \underset{i=1}{\overset{n}{}}}5c_i(8-c_i{)}^2{c}_i$ as a definite integral on the interval $0,3,$ where $c_i$ is any point in the $i^{in}$ subinterval.

A$.{\displaystyle \underset{0}{\overset{c_i}{}}}5c_i(8-c_i{)}^2{x}_i$

B$.{\displaystyle \underset{3}{\overset{0}{}}}5x^2(8-x{)}^{3}dx$

C$.{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}5x(8-x{)}^{3}dx$

D$.{\displaystyle \underset{0}{\overset{3}{}}}5x(8-x{)}^{2}dx$

E$.{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}5c_i(8-c_i{)}^2{x}_i$