Comparison Test for Improper Integrals

In this video, I will show you how to use the comparison test to determine if an improper integral is convergent or divergent. An improper integral is convergent if the the result of solving the integral produces a constant number, and it is divergent if the result is infinity. But sometimes it is not possible to solve the improper integral by hand, like we did in the previous video. Instead, you must use the comparison test theorem for improper integrals which takes a shortcut in four steps and the comparison test tells you if the improper integral is convergent or divergent. This is a concept which is important in Calculus 2.

I like to use the FEP-NL-SL-C acronym to remember which function is greater than which one. That means as x approaches infinity,
Factorial greater than
Exponential greater than
Polynomial (of any degree) greater than
XlogX greater than
Linear greater than
Square root (or x to the power of a constant between 0 and 1) greater than
Logarithms greater than
Constant.
I know that seems like a lot, but it is so useful to me on many exams. Let me know if this makes sense and please buy me coffee by subscribing :) It means a lot

SOLUTIONS TO THE PROBLEMS:

In the next video, I will show you how to find the arc length of a function.

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[AndreaFerro-ksbp]

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Truly appreciate those extra problems!

[vivienshaanika]

You are a good tutor, this is amazing and continue doing your best 🙌🙌👏👏👏

[nutritionbyelsa]

epic resource, thank you so much, so hard to find high quality resources on advanced math topics, sharing with my calc class at UBC, thank you : )

[yonghoon]

Thank you! Your videos are very helpful and you explain all that complicated math with a smile on your face, amazing!

[voltaire]

We love you Dat, cant imagine life without you

[tailingoff]

Thanks for showing the counter example and also letting me know that hit and trial is the way we approach these tests. 😊

[Evelyn-oyli]

Thank you so much, finally i could understand this topic after confusing during class. Thankyou 🥺🥺🥺

[sahilbhagat]

Thank you very much to clearing concepts so easily.

[mrmansir]

very well made videos. I liked your improper integral video too

[bilgexo]

i hope you live happily forever. thank u for the video

[HanifaNasala]

Thank you, it's very easy to follow and understand😊

[sa_]

Greetings from the University of Florida. Have a Midterm in Calc 2 in 2 days 😅 Thank you a lot

[bossbabe]

Hi, thank you for this video! I have just one question, how do you determine the function g(x)? How do I know which function to use to compare to f(x)?

[md.ashrafulislamsami]

Great video! I have a question. Most of the time, I get stuck on step step 3, you showed exponensial > linear ..In step 3, how can we easily calculate which is greater/smaller than there any chart or video related to it..That would be great help..Thank you.

[emberlynnguyen]

Your explanations are really comprehensible! Thank you so much!

[bhtkyav]

thank youuu everything is clear noww :)

[ssamirs]

What happens if the numerator is not always positive?

[kudakwashemcmillengomba]

Watching this video a few minutes before my test😮....Will come and give some feedback after😂