In this video I go over the use of tables of integrals when integrating functions. Integration using tables of integrals has been widely used in the past before the internet was fully developed and integration computer algebra systems (CAS) were widely available online. That being said they are useful when you don't have an CAS available or your internet connection is not working. In this video I go over the example of finding the volume of the region bounded by the functions y = arctan(x), y = 0 and x = 1 and rotated about the y-axis. The problem involves solving an integral with an integrand of the form u*arctan(u). Luckily the integral of such an integral can be found in formula number 92 in the Table of Integrals found in my calculus book as well as through this link: https://tinyurl.com/integralsmes.
Watch Video On:
- DTube: https://d.tube/#!/v/mes/QmPouUZDYVwJ75wqHMdDBdxwUcECraukLdkNs8U3DbBGz4
- BitChute: https://www.bitchute.com/video/w4qrBTfZM4zA/
- YouTube: https://youtu.be/AOToFP-4Mfg
Download Video Notes: http://1drv.ms/1JM5hyZ
View Video Notes Below!
Reuse of My Videos:
- Feel free to make use of / re-upload / monetize my videos as long as you provide a link to the original video.
Fight Back Against Censorship:
- Bookmark sites/channels/accounts and check periodically
- Remember to always archive website pages in case they get deleted/changed.
Join my private Discord Chat Room: https://mes.fm/chatroom
Check out my Reddit and Voat Math Forums:
Buy "Where Did The Towers Go?" by Dr. Judy Wood: https://mes.fm/judywoodbook
Follow My #FreeEnergy Video Series: https://mes.fm/freeenergy-playlist
Watch my #AntiGravity Video Series: https://steemit.com/antigravity/@mes/series
- See Part 6 for my Self Appointed PhD and #MESDuality Breakthrough Concept!
NOTE #1: If you don't have time to watch this whole video:
- Skip to the end for Summary and Conclusions (If Available)
- Play this video at a faster speed.
-- TOP SECRET LIFE HACK: Your brain gets used to faster speed. (#Try2xSpeed)
-- Try 4X+ Speed by Browser Extensions or Modifying Source Code.
-- Browser Extension Recommendation: https://mes.fm/videospeed-extension
-- See my tutorial to learn more: https://steemit.com/video/@mes/play-videos-at-faster-or-slower-speeds-on-any-website
- Download and Read Notes.
- Read notes on Steemit #GetOnSteem
- Watch the video in parts.
NOTE #2: If video volume is too low at any part of the video:
- Download this Browser Extension Recommendation: https://mes.fm/volume-extension
Integration using Tables of Integrals: Example 1
Tables of indefinite integrals are very useful when we are confronted by an integral that is difficult to evaluate by hand and we don't have access to a computer algebra system (CAS); in other words, in the case we don't have internet access as there are many online CAS calculators
I will be using the Table of Integrals found in my calculus book and you can view that table by going to the URL: https://tinyurl.com/integralsmes
It should be remembered that often times that integrals do not occur exactly in the form listed in a table.
- Usually we need to use substitution or algebraic manipulation to transform a given integral into one of the forms in the table.
The region bounded by the curves y = arctan(x), y = 0, and x = 1 is rotated about the y-axis. Find the volume of the resulting solid.