Integrals and Volumes by Cylindrical Shells
In this video I go over an introduction to solving the volume of a solid formed by rotating a region about a line using the method of Cylindrical Shells. This method is useful when dealing with functions that make the volume integral difficult to solve when using the earlier methods which I covered in my earlier videos.
Watch Video On:
- DTube: https://d.tube/#!/v/mes/QmQKh7wHW1kipx1d35uocXorjfT6UT6F93Hmg6sPty2zSJ
- BitChute: https://www.bitchute.com/video/hd5MuzpxPSuS/
- YouTube: https://youtu.be/LbywV9X154E
Download Video Notes: http://1drv.ms/1wFaWq1
View Video Notes Below!
Download These Notes: Link is in Video Description.
View These Notes as an Article: https://steemit.com/@mes
Subscribe via Email: http://mes.fm/subscribe
Donate! :) https://mes.fm/donateReuse 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 along my epic video series:
- #MESScience: https://mes.fm/science-playlist
- #MESExperiments: https://steemit.com/mesexperiments/@mes/list
- #AntiGravity: https://steemit.com/antigravity/@mes/series
-- See Part 6 for my Self Appointed PhD and #MESDuality Breakthrough Concept!- #FreeEnergy: https://mes.fm/freeenergy-playlist
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
Integrals and Volumes by Cylindrical Shells
Some volume problems are very difficult to handle with the methods in my earlier videos. For example consider obtaining volume of the shape formed by rotating the region below about the y-axis.
Method of Cylindrical Shells
Easy way to remember: V = circumference x height x thickness
Now consider the volume of the solid obtained by rotating the region below about the y-axis.
Now this seems reasonable but a formal proof of this will be shown in a later video once I cover the concept of integration by parts.
The best way to remember using the cylindrical shells formula is to flatten a shell as shown below.