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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 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}

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \begin{align} 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{align} }