6.5 Average Value of a Function/15

\begin{align}

The table gives values of a continuous function. Use the Midpoint Rule to estimate the average value of $f$ on $[20,50]$.\\

\begin{tabular*}{0.75\textwidth}{@{\extracolsep{\fill} } | c | c | c | r | }

 \hline
 label 1 & label 2 & label 3 & label 4 \\
 \hline 
 item 1  & item 2  & item 3  & item 4  \\
 \hline

\end{tabular*}

\end{align}

${\begin{aligned}f_{avg}&={\frac {1}{30}}\int _{20}^{50}f(x)dx\\[2ex]&={\frac {1}{30}}\left[10{\bigg (}f(25)+f(35)+f(45){\bigg )}\right]={\frac {1}{3}}{\bigg (}38+29+48{\bigg )}\\[2ex]&={\frac {115}{3}}\\[2ex]&=38{\frac {1}{3}}\end{aligned}}$