1 / 1

Analysis of the Convergence of an Improper Integral Using the Comparison Test

This solution evaluates whether a specific improper integral converges or diverges by employing the Comparison Test. It is established that for ( x geq 3 ), ( ln x leq x ln x ). Previous work demonstrated that the improper integral diverges when assessed in Example 4.9.7 (5). Based on the Comparison Test principles, it is concluded that if a larger improper integral is confirmed to diverge, the subject integral must also exhibit divergence.

barbie
Download Presentation

Analysis of the Convergence of an Improper Integral Using the Comparison Test

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. Example 1 Determine whether the improper integral converges or diverges. Solution Since ln x  xln x for x  3, it follows that for x  3. In Example 4.9.7 (5), we showed the improper integral diverges. By the Comparison Test, the larger improper integral must also diverge.

More Related