Short Question about improper integrals:

In summary, an improper integral is an integral with infinite limits of integration or a vertical asymptote within the interval of integration. There are two types, Type 1 and Type 2. To evaluate an improper integral, a limit can be used or the comparison test and fundamental theorem of calculus. A convergent improper integral has a finite limit, while a divergent one has an infinite or non-existent limit. Improper integrals can be solved using regular integration techniques, with some additional steps needed for the infinite limits or vertical asymptotes.
  • #1
Edwardo_Elric
101
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
 
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  • #2
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.
 

1. What is an improper integral?

An improper integral is an integral where either the upper or lower limit of integration is infinite, or the integrand has a vertical asymptote within the interval of integration. It is also referred to as an unbounded integral.

2. What are the types of improper integrals?

The two types of improper integrals are Type 1, where the upper or lower limit of integration is infinite, and Type 2, where the integrand has a vertical asymptote within the interval of integration.

3. How do you evaluate an improper integral?

To evaluate an improper integral, you can use a limit as the upper or lower limit of integration approaches infinity, or you can use the comparison test or the limit comparison test to determine if the integral converges or diverges. If it converges, you can then use the fundamental theorem of calculus to evaluate it.

4. What is the difference between a convergent and a divergent improper integral?

A convergent improper integral is one where the limit of the integral as the upper or lower limit approaches infinity exists and is a finite number. A divergent improper integral is one where the limit does not exist or is infinite.

5. Can improper integrals be solved using regular integration techniques?

Yes, improper integrals can be solved using regular integration techniques like substitution, integration by parts, and partial fractions. However, some additional steps may be required to handle the infinite limits or vertical asymptotes.

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