Applying Integral Test: Why did they integrate from 1 to ∞ instead of

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SUMMARY

The discussion centers on the application of the Integral Test in calculus, specifically addressing why integration is performed from 1 to ∞ rather than from e to ∞. Participants emphasize the importance of understanding the theorem presented in the textbook regarding the Integral Test, which provides the necessary conditions for convergence. Example 4 in the attachment serves as a critical reference point for this analysis, illustrating the practical application of the theorem in determining convergence of series.

PREREQUISITES
  • Understanding of the Integral Test in calculus
  • Familiarity with convergence and divergence of series
  • Basic knowledge of improper integrals
  • Ability to interpret mathematical examples from textbooks
NEXT STEPS
  • Review the theorem on the Integral Test in your calculus textbook
  • Examine Example 4 in the context of convergence criteria
  • Practice solving problems involving improper integrals
  • Explore related convergence tests such as the Comparison Test
USEFUL FOR

Students of calculus, educators teaching integral calculus, and anyone looking to deepen their understanding of convergence tests in mathematical analysis.

InvalidID
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Consider example 4 in the attachment.

Why did they integrate from 1 to ∞ instead of e to ∞?
 

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InvalidID said:
Consider example 4 in the attachment.

Why did they integrate from 1 to ∞ instead of e to ∞?
Your textbook must have a theorem in which they present the integral test. Find it and see what it says.
 

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