In this video I go over another example on solving the volume of a shape using the method of cylindrical shells. The example in this video is finding the volume of the solid formed by rotating about the y-axis the region between y = x and x = x². In my earlier videos I solved this example using other methods but this time I show how it is easier to use the method of cylindrical shells to find the volume.

Watch Video On:

• DTube: https://d.tube/#!/v/mes/QmYDpnHFkdeoMvMrLFEnMSFH1qFNJz7sSKns8PjYneTHb6
• BitChute: https://www.bitchute.com/video/xgLMGpyDgpPK/
• YouTube: https://youtu.be/hR-GcP-XpD4

Download Video Notes: http://1drv.ms/1xsRxce

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/donate

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:

• Reddit: https://reddit.com/r/AMAZINGMathStuff
• Voat: https://voat.co/v/AMAZINGMathStuff

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 Example 2

Example:

Find the volume of the solid obtained by rotating about the y - axis the region between y = x and y = x².

Solution: