Using the $R_N$ approximation, express the area under the graph $f(x)=8sin(x)$ over $0,\frac{}{3}$ as a limit$.$

Select the correct value.

$\underset{N}{lim}{\displaystyle \underset{j=1}{\overset{N}{}}}\frac{3}{8N}sin(\frac{j}{3N})$

$\underset{N}{lim}{\displaystyle \underset{j=0}{\overset{N-1}{}}}\frac{8}{N}sin(\frac{j}{3N})$

$\underset{N}{lim}{\displaystyle \underset{j=0}{\overset{N-1}{}}}\frac{8}{3N}sin(\frac{j}{3N})$

$\underset{N}{lim}{\displaystyle \underset{j=0}{\overset{N-1}{}}}\frac{3}{8N}sin(\frac{j}{3N})$

$\underset{N}{lim}{\displaystyle \underset{j=1}{\overset{N}{}}}\frac{8}{3N}sin(\frac{j}{3N})$