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>. \\ | 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| | [[File:Tablefor15.png|300px|left]] | ||
<math> | <math> | ||
Revision as of 02:09, 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)