1 / 31

Understanding Improper Integrals: Types, Definitions, and Examples

Learn about improper integrals of Type I and Type II, including convergent and divergent limits, with detailed examples and memorization tips for better understanding. Master the concept for Chapter 10 with practical applications.

shirleynelson
Download Presentation

Understanding Improper Integrals: Types, Definitions, and Examples

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. IMPROPER INTEGRALS Improper Integral TYPE-II: Discontinuous Integrand Integrands with Vertical Asymptotes TYPE-I: Infinite Limits of Integration Example Example

  2. IMPROPER INTEGRALS DEFINITION OF AN IMPROPER INTEGRAL OF TYPE 1 Example

  3. IMPROPER INTEGRALS Example DEFINITION OF AN IMPROPER INTEGRAL OF TYPE 1

  4. IMPROPER INTEGRALS DEFINITION OF AN IMPROPER INTEGRAL OF TYPE 1 The improper integrals are called convergentif the corresponding limit exists and divergent if the limit does not exist.

  5. IMPROPER INTEGRALS DEFINITION OF AN IMPROPER INTEGRAL OF TYPE 1 Example

  6. IMPROPER INTEGRALS DEFINITION OF AN IMPROPER INTEGRAL OF TYPE 1 convergent If both improper integrals are convergent Example

  7. IMPROPER INTEGRALS Memorize: (We need it for chapter10) Example

  8. IMPROPER INTEGRALS Improper Integral TYPE-II: Discontinuous Integrand Integrands with Vertical Asymptotes TYPE-I: Infinite Limits of Integration Example Example

  9. IMPROPER INTEGRALS DEFINITION OF AN IMPROPER INTEGRAL OF TYPE 2

  10. IMPROPER INTEGRALS

  11. IMPROPER INTEGRALS DEFINITION OF AN IMPROPER INTEGRAL OF TYPE 2

  12. IMPROPER INTEGRALS

  13. IMPROPER INTEGRALS DEFINITION OF AN IMPROPER INTEGRAL OF TYPE 2 Example

  14. IMPROPER INTEGRALS DEFINITION OF AN IMPROPER INTEGRAL OF TYPE 2 Example

  15. IMPROPER INTEGRALS Example Example

  16. IMPROPER INTEGRALS Example

  17. IMPROPER INTEGRALS (If bigger convg  smaller convg) (If smaller divg  bigger divg)

  18. IMPROPER INTEGRALS

  19. IMPROPER INTEGRALS F112

  20. IMPROPER INTEGRALS 082

  21. IMPROPER INTEGRALS F092

  22. IMPROPER INTEGRALS

  23. IMPROPER INTEGRALS F092

  24. IMPROPER INTEGRALS F102

More Related