diff --git a/.obsidian/plugins/obsidian-git/data.json b/.obsidian/plugins/obsidian-git/data.json index e69de29..bef4c6e 100644 --- a/.obsidian/plugins/obsidian-git/data.json +++ b/.obsidian/plugins/obsidian-git/data.json @@ -0,0 +1,27 @@ +{ + "commitMessage": "vault backup: {{date}}", + "autoCommitMessage": "vault backup: {{date}}", + "commitDateFormat": "YYYY-MM-DD HH:mm:ss", + "autoSaveInterval": 5, + "autoPushInterval": 0, + "autoPullInterval": 5, + "autoPullOnBoot": true, + "disablePush": false, + "pullBeforePush": true, + "disablePopups": false, + "listChangedFilesInMessageBody": false, + "showStatusBar": true, + "updateSubmodules": false, + "syncMethod": "merge", + "customMessageOnAutoBackup": false, + "autoBackupAfterFileChange": false, + "treeStructure": false, + "refreshSourceControl": true, + "basePath": "", + "differentIntervalCommitAndPush": false, + "changedFilesInStatusBar": false, + "showedMobileNotice": true, + "refreshSourceControlTimer": 7000, + "showBranchStatusBar": true, + "setLastSaveToLastCommit": false +} \ No newline at end of file diff --git a/education/math/MATH1210 (calc 1)/Integrals.md b/education/math/MATH1210 (calc 1)/Integrals.md index 9b23664..bd7eb56 100644 --- a/education/math/MATH1210 (calc 1)/Integrals.md +++ b/education/math/MATH1210 (calc 1)/Integrals.md @@ -87,8 +87,10 @@ Average = $\dfrac{1}{b-a} \int_a^b f(x)dx$ Let $f$ be a continuous function on the closed interval $[a, b]$ and let $F$ be any antiderivative of $f$, then: $$\int_a^b f(x) dx = F(b) - F(a)$$ ## Proof - ## Mean Value Theorem Between the interval $[a, b]$, the average rate of change of a function **must be equal** to at least one point between $[a, b]$: $$ f'(c) = \dfrac{f(b) - f(a)}{x-a} $$ -For some $c$ between $a$ and $b$. \ No newline at end of file +For some $c$ between $a$ and $b$. + +1. $F(b) - F(a) = F(x_1) - F(x_0)$ +2. $= (F(x_1) - F(x_0) + (F(x_2) - F(x_1) + (F(X_3) - F(X_2) + \cdots + (F(x_n) - f(x_{n - 1})$ 3. $= \ No newline at end of file