Comparison Test for Improper Integrals

The comparison test let's us deduce the convergence or divergence of some improper integrals by relating a complicated function that is challenging to a simpler one we can do. If we compare two functions f(x) greater than g(x) greater than 0, we can deduce things about the convergence of the improper integrals. If the larger integral converges from 1 to infinity, then the smaller one must as well. Likewise, if the smaller one diverges, then the bigger one diverges.

We specifically focus on integrals of 1/x^p, which we know precisely when it converges and diverges. Then if there is a more complicated rational function, we can compare it to this.

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This video was created by Dr. Trefor Bazett, an Assistant Professor, Educator at the University of Cincinnati.

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[elielrios]

College calculus midterm tomorrow and I’m cramming this sections, it made no sense until now. Thanks a lot!

edit: I got an 82%

[piecheeseboy]

Had you last semester for calc one, amazing teacher thank you!

[jean-philippefranko]

Thank you for breaking down all the thought processes, especially about finding a simpler function for carrying the convergence test [5:15]. Also great job about the way you use the colors ! That really helps to drive the attention toward the main aspects of each situation. I love your work !

[babooshkabatoosh]

This was, seriously, an excellent explanation!

[mdrakibhossain]

Now it's clear to me. This topic was somehow so ambiguous to me. Thanks man .

[chao_laura]

My first time here and I swear you are a life saver 🥺 where have you been all my life 😩

[konakill]

This hasn't clicked for the past week and a half, thank you for the help!

[humidifier]

thank you so much, wild how this 8 min video is better than any of my calculus lectures

[dantellez]

thanks sooo much!!! I had such a hard time trying to get this concept. You explained it so cool and easy to understand. Here you have your Like, good man.

[mike_the_tutor]

There's a bit of audio clipping here, but other than that this video is a great introduction to the comparison test. Thanks for sharing.

[zest]

Glad I stumbled onto this, it makes this concept a lot easier to understand

[qedmath]

Nice video! You explain this stuff extremely well.
At 6:32, we can use partial fraction, and arrive at -ln|x+1| + 1/2ln|x^2 - x + 1| - 1/sqrt(3)*arctan(2x/sqrt(3)) + C.

[amansingh-wwqc]

Sir u are great, I can't believe someone can teach this good for free, I really love u really really really

[ice-nwps]

I have a midterm in an hour and ah this thing is not easy to keep in mind

[SW-]

Great video, helped a lot. P.S. You kinda look like an off-brand doctor strange. lol

[rockyboy]

Finally, I understood what it means. Thank you.

[endv--]

If the bounds are from 2 to infinity, instead of 1 to infinity, would the P convergence change to P > 2?

[harmandeepsingh]

Sir you are doing amazing jobs👍thanku so much

[naderbenammar]

damn you are a very good teacher ! thx it helped a lot

[saeedahamad]

My calculus midterm is in two hours and someone sent me this video saying I will understand after watching this, and indeed I do now thank you so much<3