vault backup: 2025-04-15 10:01:58

.obsidian/plugins/obsidian-git/data.json

@@ -0,0 +1,27 @@
+{
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+  "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
+}

education/math/MATH1210 (calc 1)/Integrals.md

@@ -184,4 +184,9 @@ $$ L =\int_a^b \sqrt{1 + f'(x)^2} dx$$
 1. $y$ has a domain of $[-1, 1]$
 2. $y' = \dfrac{1}{2}(1-x^2)^{-1/2}(-2x)$
 3. $= -\dfrac{x}{\sqrt{1 - x^2}}$
-4. $L = \int_{-1}^1 \sqrt{1 + (-\frac{x}{\sqrt{1-x^2}})}$ 
+4. $L = \int_{-1}^1 \sqrt{1 + (-\dfrac{x}{\sqrt{1-x^2}})^2}dx$ 
+5. $L = \int_{-1}^1 \sqrt{1 + \dfrac{x^2}{1-x^2}}dx$ 
+6. $L = \int_{-1}^1 \sqrt{\dfrac{1}{1-x^2}}dx$ 
+7. $L = \int_{-1}^1 \dfrac{1}{\sqrt{1-x^2}}dx$ 
+8. $L = \arcsin(x) \Big|_{-1}^1$ 
+9. $\arcsin($