1 / 8

HAVING FUN WITH ANTI-DERIVATIVES

HAVING FUN WITH ANTI-DERIVATIVES. Actually, the first thing we are going to do is to demonstrate a neat formula, namely the statement: Here is why: let be an anti-derivative of . Then, by the FTC, version 2 (we called it a corol-lary !) .

ginny
Download Presentation

HAVING FUN WITH ANTI-DERIVATIVES

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. HAVING FUN WITHANTI-DERIVATIVES Actually, the first thing we are going to do is todemonstrate a neat formula, namely the statement: Here is why: let be an anti-derivative of . Then, by the FTC, version 2 (we called it a corol-lary !)

  2. (Don’t be upset by Sam and Sue, we will give them proper names later!) So Let’s give Sam and Sue their proper names, And re-write the formula above as

  3. (ready?) But now, by the chain rule and

  4. The moral of this story is: • When taking the derivative of an integral • Use the FTC (evaluate the integrand properly) • But don’t forget the chain rule ! Here is an example:

  5. Another example: Do a few more from the textbook.

  6. Anti-derivative is an ugly word ! Using the con-nection between anti-derivatives and integrals provided by the FTC we write or more conventionally for any one anti-derivative of and call it the indefinite integral of a much better name! Now we get a few bricks and some mortar. We start with the mortar (rules)

  7. (very few) Now the bricks (depends on your memory !)

  8. and from trigonometry Any more ?

More Related