6.5 Average Value of a Function/15: Difference between revisions
Jump to navigation
Jump to search
No edit summary |
No edit summary |
||
| Line 1: | Line 1: | ||
\begin{align} | \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>. | 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>. \\ | ||
[[File:Tablefor15.png|300px|left]] | [[File:Tablefor15.png|300px|left]] | ||
\end{align} | |||
<math> | <math> | ||
Revision as of 02:10, 25 November 2022
\begin{align} The table gives values of a continuous function. Use the Midpoint Rule to estimate the average value of on . \\
![{\displaystyle [20,50]}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/5a06768fcaac877b2907129f3b9e651f4c3aafc6)
\end{align}
![{\displaystyle {\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}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/47f20d16a200f723fb32081c7357553ecea39729)