Improper Integrals: Check Answers & Get Feedback

• mat331760298
In summary, the given integrals both have the same integrand, but different limits of integration. The first integral from 1 to infinity diverges, while the second integral from 0 to 1 converges to ln|3/2|. The mistake in the original answers was due to a miscalculation in the integration process.

mat331760298

1. Determine whether the following diverges or converges. If converges, evaluate it.
a) integral from 1 to infinity of: 1/(2x^2 + x) dx
b) integral from 0 to 1 of: 1/(2x^2 + x) dx

I just want to check my answers. I got a) diverges and b) converges with value of ln|3/2|. Do these answers sound right? I would appreciate some feedback, thanks.

You had a 50/50 chance and you blew it ;)

How did you got to your conclusions?

Basically you need to find an upper/lower bound (i.e. a simpler integral that you know how to evaluate) and show that the bound converges/diverges then the original integral also converges/diverges.

i don't see how the answers are opposite lol maybe someone can show me a) so i can compare to my work

mat331760298 said:
i don't see how the answers are opposite lol maybe someone can show me a) so i can compare to my work

You haven't shown your work yet. If you do that maybe we can figure out what's wrong.

haha looked it over and when i did integration i had ln(x) + ln(2x+1) instead of ln(x) - ln(2x+1). makes sense now

1. What is an improper integral?

An improper integral is a type of integral where one or both of the limits of integration are infinite or the integrand function is not defined at some points within the interval of integration.

2. How do I know if an integral is improper?

An integral is considered improper if any of the following conditions are met: the upper or lower limit of integration is infinite, the integrand function is not defined at some points within the interval of integration, or the integrand function approaches infinity at some point within the interval of integration.

3. How do I solve an improper integral?

To solve an improper integral, you must first determine if the integral is convergent or divergent. If it is convergent, you can use a variety of techniques such as substitution, integration by parts, or partial fractions to evaluate the integral. If it is divergent, you can use the limit comparison test or the p-series test to determine the behavior of the integral.

4. Can I use a calculator to evaluate improper integrals?

Yes, depending on the complexity of the integral, you can use a graphing or scientific calculator to evaluate improper integrals. However, it is important to understand the concepts and techniques used to evaluate improper integrals in order to use a calculator effectively.

5. What is the importance of checking my answers and getting feedback for improper integrals?

Checking your answers and getting feedback is important because improper integrals can be tricky and it is easy to make mistakes. By checking your answers and getting feedback, you can ensure that your solution is correct and also identify any errors you may have made in your calculations. This can help improve your understanding of the concepts and techniques used to evaluate improper integrals.