Short Question about improper integrals:

  • Thread starter Thread starter Edwardo_Elric
  • Start date Start date
  • Tags Tags
    Integrals Short
Click For Summary
SUMMARY

This discussion focuses on the evaluation of improper integrals, specifically when one limit is divergent and the other is indeterminate. It concludes that both limits must converge for the integral to be considered convergent. If the first limit diverges, the second limit should be evaluated using L'Hôpital's Rule (LHR) to determine the overall behavior of the integral. The consensus is that if both limits diverge, the integral is automatically divergent.

PREREQUISITES
  • Understanding of improper integrals
  • Familiarity with L'Hôpital's Rule (LHR)
  • Knowledge of limits and convergence in calculus
  • Basic principles of integral calculus
NEXT STEPS
  • Study the application of L'Hôpital's Rule in various contexts
  • Explore examples of improper integrals with divergent and indeterminate limits
  • Learn about convergence tests for integrals
  • Investigate advanced topics in integral calculus, such as Lebesgue integration
USEFUL FOR

Students and educators in calculus, mathematicians dealing with integrals, and anyone looking to deepen their understanding of improper integrals and convergence criteria.

Edwardo_Elric
Messages
101
Reaction score
0
Hi

I was Just hoping to ask a short question about improper integrals ...

when there are two limits in the integral: the 1st limit is divergent but the second limit is indeterminate... can it be automatically divergent? or do you need to evaluate first the second limit using LHR? so that both limits becomes divergent
 
Physics news on Phys.org
if it has 2 limits then yes both limits MUST converge.
so if you're lucky and get the limit that diverges you can just move on to other problems quicker.
 

Similar threads

Determine if the improper integral is divergent or not
  • · Replies 2 ·
Replies
2
Views
2K
Two ways of integration giving different results
  • · Replies 9 ·
Replies
9
Views
2K
Does the series converge using the integral test?
  • · Replies 16 ·
Replies
16
Views
4K
Improper Integral: Convergence and Divergence Analysis for 1/(1-x) from 0 to 2
  • · Replies 7 ·
Replies
7
Views
7K
Question re: Limits of Integration in Cylindrical Shell Equation
  • · Replies 24 ·
Replies
24
Views
3K
Finding k in a probability density function
  • · Replies 4 ·
Replies
4
Views
4K
Generalize improper integral help
  • · Replies 1 ·
Replies
1
Views
1K
How would we integrate this without using double integrals?
  • · Replies 10 ·
Replies
10
Views
2K
Evaluate the Improper integral [4,13] 1/(x-5)^(1/3)
  • · Replies 1 ·
Replies
1
Views
2K
Convergence of Improper Integral with Limit Evaluation
  • · Replies 3 ·
Replies
3
Views
2K