COMPARISON THEOREM WILL FINALLY MAKE SENSE!

► My Integrals course: www.kristakingmath.com/integr...
You can use the comparison theorem to say whether an improper integral converges or diverges. You'll learn about the comparison theorem when you study integrals, but also when you study sequences and series.
Your goal is to find a function that's really similar to the function you're given, and then compare the two. If you can find a function that you know is always larger than the original function, and that comparison function converges, then you've proven that the original function converges.
On the other hand, if you can find a function that you know is always smaller than the original function, and that comparison function diverges, then you've proven that the original function diverges.
In other words, you're trying to find a smaller function and show that it diverges, or find a larger function and show that it converges.
● ● ● GET EXTRA HELP ● ● ●
If you could use some extra help with your math class, then check out Krista’s website // www.kristakingmath.com
● ● ● CONNECT WITH KRISTA ● ● ●
Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)
Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”
So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student-from basic middle school classes to advanced college calculus-figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: www.kristakingmath.com
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[@haroldh6678]

Those diagrams in the introduction make the difference compared to all the other videos. Thanks again Krista ! : )

[@marc1476]

Your explanations are so clear!! Thank you so much! Your videos are saving me right now

[@kristakingmath]

So glad they're helping! Thanks for letting me know. :)

[@Scarppegios]

Wish you hadn't used a known interval like sine because the problem I've been having is determining the interval but the initial explanation about the basic concept was greatl

[@nycityzen]

Thanks. You cover every single topic. I could only find comparison tests for series :)

[@divinemadu4340]

Simply Amazing...Thanks

[@valroe7034]

i dont think you can understand how much i love you

[@picknikbasket]

I wasn't familiar with that theorem but I'm much more comfortable with it now, thanks Krista!

[@kristakingmath]

+picknikbasket You're welcome, happy to help!

[@markbenn1907]

Great graphic explanation!! WE NEED THAT!!

[@kristakingmath]

Thanks, Mark! I'm glad it made sense! :)

[@danguerro3818]

very clear

[@ycap7028]

great video thanks!

[@kristakingmath]

Thanks, Ryan, so glad you liked it! :)

[@gdr733]

Krista Love your videos....but i just had another question. Do you know any good physics videos? Mechanics to be specific.

[@kristakingmath]

Unfortunately I don't watch a lot of physics videos, so there isn't a channel I'd recommend specifically. Sorry about that!

[@matildawillcox1693]

Wonderful!

[@kristakingmath]

Thanks, Matilda! :D

[@QuackAttackYT]

Thanks, I have an exam in two days. Please make more calculus tutorials. They're no bs and well put together.

[@kristakingmath]

Thanks, Steez, I'm so glad they're helping! I hope the exam went great! :D

[@xs2278]

You are the best

[@AdrienneSmackoff21]

You're so amazing! This made so much sense!

[@kristakingmath]

Oh good! So glad it helped! :D

[@esamh1640]

Really great

[@kristakingmath]

+Esam H Thanks Esam!

[@bahaatamer1245]

this video did make a lot of sense, but please do respond if possible. For this function, it was between 0 and 1 due to the sin^2(x) curve limits, but for different functions it gets extremely confusing of what to compare it to. Any tips please?

[@kristakingmath]

That's a really tough question, because it'll be different for every function. In general, one trick is to look for a function that's like yours, but simpler. For example, if you only take the most significant term, or you take out constants, etc. Unfortunately this just takes practice! :)

[@n.richardanoliefo3950]

that thumbnail though

[@buongiorno5233]

She’s adorkable

[@samirt1976]

mam... which software you use to write.. please guide mam...

[@kristakingmath]

Hey, Samir! It's called Sketchbook.

[@NguyenKunThomas]

but what about the p therom? p =1/2

[@mauriciocantu6745]

I'm guessing the p theorem only hold true when the upper limit of integration is infinity. In this case the integral goes from 0 to pi, hence why it converges. I might be wrong though

[@WiskundeTraining]

Best explanation on youtube👏👏👏

[@kristakingmath]

Thank you so much, Alisha! :)

[@Angel_4501]

And the integral: from 0 to pi, 1/sqrt(1 - sinx) dx Converges or diverges?

[@carultch]

It diverges.

[@Angel_4501]

@@carultch Thanks, you're three years late

[@Ben61539]

At 3:48 you said cosine oscillates back and forth b/w 0 and 1. Then you said cosine oscillates back and forth b/w -1 and 1. Which is it? The second one I'm guessing?

[@kristakingmath]

Sorry about that... it oscillates back and forth between -1 and 1. :)

[@dv4346]

Great video but it still didn't make sense for some reason :/

[@rebeltime6413]

isn't pi an infinite number? wouldn't that mean it diverges?

[@carultch]

Pi is not an infinite number. It is more like "in-between-finite" than infinite. In that no matter what rational number you choose to approximate it, it is always in between that rational number and another rational number, and will never exactly be a rational number. You could even do the same thing with algebraic numbers in place of rational numbers, and pi is in between two algebraic numbers , but never will equal an algebraic number.

[@davey7941]

You're amazing. Marry me please