arc/notes
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

vault backup: 2025-04-15 09:46:58

Browse Source
This commit is contained in:
arc 2025-04-15 09:46:58 -06:00
parent 8810f2f9cf
commit f014927f13
2 changed files with 6 additions and 30 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

27
.obsidian/plugins/obsidian-git/data.json vendored
View File

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

9
education/math/MATH1210 (calc 1)/Integrals.md
View File

@ -169,9 +169,12 @@ $$ L =\int_a^b \sqrt{1 + f'(x)^2} dx$$
5. $L = \int_{1/2}^5 \sqrt{1 + (\dfrac{4x-1}{2x^2})^2}dx$ : Use the length formula 5. $L = \int_{1/2}^5 \sqrt{1 + (\dfrac{4x-1}{2x^2})^2}dx$ : Use the length formula
6. $= \int_{1/2}^5 \sqrt{1 + \dfrac{x^8 - 2x^4 + 1}{x^4}} dx$: Apply the $^2$ 6. $= \int_{1/2}^5 \sqrt{1 + \dfrac{x^8 - 2x^4 + 1}{x^4}} dx$: Apply the $^2$
7. $= \int_{1/2}^5 \sqrt{\dfrac{4x^4 + x^8 -2x^4 + 1}{4x^4}}dx$: Set $1 = \dfrac{4x^4}{4x^4}$ and add 7. $= \int_{1/2}^5 \sqrt{\dfrac{4x^4 + x^8 -2x^4 + 1}{4x^4}}dx$: Set $1 = \dfrac{4x^4}{4x^4}$ and add
8. $= \int_{1/2}^5 \sqrt{\dfrac{x^8 + 2x^4}{4x^4}}dx$ 8. $= \int_{1/2}^5 \sqrt{\dfrac{x^8 + 2x^4 + 1}{4x^4}}dx$: Factor the numerat
9. $\int_{1/2}^5 \sqrt{\dfrac{(4x+1)^2}{4x^4}}$ 9. $= \int_{1/2}^5 \sqrt{\dfrac{(4x+1)^2}{4x^4}}dx$
10. = $\int_{1/2}^5 \dfrac{x^4 + 1}{2x^2}dx$ 10. = $\int_{1/2}^5 \dfrac{x^4 + 1}{2x^2}dx$
11. $= \frac{1}{2}\int_{1/2}^5 \dfrac{x^4 + 1}{x^2}$ 11. $= \frac{1}{2}\int_{1/2}^5 \dfrac{x^4 + 1}{x^2}$
12. $= \dfrac{1}{2} \int_{1/2}^5 (x^4 + 1)(x^{-2})dx$ 12. $= \dfrac{1}{2} \int_{1/2}^5 (x^4 + 1)(x^{-2})dx$
13. $= \frac 1 2 \int_{1/2}^5 (x^2 - x^$ 13. $= \frac 1 2 \int_{1/2}^5 (x^2 - x^{-2})dx$
14. $= \dfrac{1}{2} (\frac{1}{3}x^3 - x^-1)\Big|_{1/2}^5$
15. $= (\frac{125}{6} - \frac{1}{10}) - (\frac{1}{48} - 1)$
16. $=(\frac{5000}{240} - \frac{24}{240}) - (\frac{5}{240} - \frac{240}{240})$