1 / 10

Improper Integrals with Infinite Limits of Integration

Improper Integrals with Infinite Limits of Integration. Improper Integrals with Infinite Limits of Integration. Integrals that have one or both integrands as infinity are improper integrals. To get an idea of how to evaluate an improper integral, consider the integral.

carriemoore
Download Presentation

Improper Integrals with Infinite Limits of Integration

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 with Infinite Limits of Integration

  2. Improper Integrals with Infinite Limits of Integration Integrals that have one or both integrands as infinity are improper integrals. To get an idea of how to evaluate an improper integral, consider the integral

  3. Improper Integrals with Infinite Limits of Integration This integral can be interpreted as the area of the shaded region shown Taking the limit as b  produces

  4. Improper Integrals with Infinite Limits of Integration

  5. Example 1 – An Improper Integral That Diverges Evaluate Solution:

  6. Example 1 – Solution cont’d See Figure 7.14. Figure 7.14

  7. Examples

  8. Improper Integrals with Infinite Discontinuities The second basic type of improper integral is one that has an infinite discontinuity at or between the limits of integration.

  9. Example 5 – An Improper Integral with an Infinite Discontinuity Evaluate Solution: The integrand has an infinite discontinuity at x = 0, as shown in Figure 7.19. You can evaluate this integral as shown below. Figure 7.19

  10. Examples

More Related