1 / 8

8.2 Integration By Parts

8.2 Integration By Parts. That is, what to do when integrating a product. There are times that the tricks we have learned so far won’t work. What happens when you need to integrate a product? That is, something that fits the pattern Such as. What is the derivative of a product?.

aden
Télécharger la présentation

8.2 Integration By Parts

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. 8.2 Integration By Parts That is, what to do when integrating a product

  2. There are times that the tricks we have learned so far won’t work. What happens when you need to integrate a product? That is, something that fits the pattern Such as

  3. What is the derivative of a product?

  4. Integration by Parts Therefore, you will let f(x)=u and g(x)=dv. Remember: we are looking at the form

  5. How do I know which is u and which is dv? A good rule of thumb (although NOT always a guarantee) is this: u = the one that could differentiate to 0 dv = the one that can be integrated easily. This isn’t a guarantee, but it at least gives a starting place.

  6. Examples

  7. Now that last problem was quite long. There is a shortcut, called Tabular Integration, which can be used when many repetitions are needed to get to f(x) = 0 and the integration of g(x) is easy. Simply list in 2 columns the sequential derivatives of f(x) next to the sequential integrations of g(x). Use diagonal arrows (with + - + -) to connect each f(x) derivative with each g(x) integration. See next problem.

  8. + - + -

More Related