6.5 Average Value of a Function/15: Difference between revisions
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The table gives values of a continuous function. Use the Midpoint Rule to estimate the average value of <math> f </math> on <math> [20, 50] </math>. | \begin{align} | ||
The table gives values of a continuous function. Use the Midpoint Rule to estimate the average value of <math> f </math> on <math> [20, 50] </math>.\\ | |||
\begin{tabular*}{0.75\textwidth}{@{\extracolsep{\fill} } | c | c | c | r | } | \begin{tabular*}{0.75\textwidth}{@{\extracolsep{\fill} } | c | c | c | r | } | ||
\end{tabular*} | \end{tabular*} | ||
\end{align} | |||
<math> | <math> | ||
Revision as of 01:41, 25 November 2022
\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 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 [20, 50] } .\\
\begin{tabular*}{0.75\textwidth}{@{\extracolsep{\fill} } | c | c | c | r | } \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} }