6.5 Average Value of a Function/15: Difference between revisions
Jump to navigation
Jump to search
(Created page with "<math> \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} </math>") |
No edit summary |
||
| (20 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
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|330px|left]] | |||
<math> | <math> | ||
Latest revision as of 02:10, 25 November 2022
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)
![{\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)