Symmetry in Integrals: Examples

in MES Science6 years ago (edited)

In this video I go further into symmetry in integrals by going over 2 useful examples. One of the examples is integrating an even function and the other one is integrating an odd function. Using the concept of symmetry we can greatly simplify the integration so make sure to watch this video!


Watch Video On:

Download Video Notes: https://1drv.ms/b/s!As32ynv0LoaIg4I0KO5s53Db6mdYjQ?e=XvJJ4M


View Video Notes Below!


Download these notes: Link is in video description.
View these notes as an article: https://peakd.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:

Buy "Where Did The Towers Go?" by Dr. Judy Wood: https://mes.fm/judywoodbook
Follow along my epic video series:


NOTE #1: If you don't have time to watch this whole video:

NOTE #2: If video volume is too low at any part of the video:


Symmetry in Integrals Examples

Symmetry in Integrals Examples.jpeg

Recap on Integrals of Symmetric Functions Theorem

Suppose f is continuous on [-a, a].

(a) If f is even, meaning f(-x) = f(x), then:

image.png

(b) If f is odd, meaning f(-x) = - f(x), then:

image.png

Examples

image.png

image.png

image.png

image.png