How to use the INTEGRAL TEST for series

► My Sequences & Series course: www.kristaking...
The integral test is a convergence test that you can use to say whether or not a series converges. In order to figure out whether or not to use the integral test, you need to look to see whether the series you're given could turn into a function that you could integrate. If it's something you can integrate, then it might be a good candidate for the integral test.
Your goal will be to turn the series into a function, integrate that function, and then evaluate the function over the infinite integral. If you get a real number answer as a result, then the integral test proves that the series converges. If the result of the integration is an infinite answer, the the integral test proves that the series diverges. Even if the series converges, you can't use the integral test to say to which value the series converges.
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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?!”
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[@samueloladeji8830]

You are my favorite instructor on youtube. You are the best.

[@kristakingmath]

Thank you so much, Samuel! I'm honored! :)

[@alex.merical]

How are there six people who disliked this?!? I can't thank you enough Prof. King!

[@aNgLe-ng5hs]

why she is doing all the calculation when we already know that tan inverse of is (pi/4).is there anything i am missing here,any benefits of doing these calculation.please guide

[@georgesadler7830]

Professor Krista King, thank you for an excellent video/lecture on How to use the Integral Test for Series in Calculus, however equal signs are missing between the problem and the final solution. Please correct this error in the video.

[@MsEady123]

This video helped me understand how to use the integral test. Thank you.

[@nathantonning]

Great explanation!

[@kristakingmath]

+Nathan Tonning Thank you!

[@JrEra]

phenomenal video, thanks

[@kristakingmath]

You're welcome! I’m so glad you liked it!! ❤️

[@enashameed471]

Thanks جزاك الله خيرا 💜💜💜

[@redhedgehogx4076]

wow she is amazing, I want her to be my teacher forever

[@amanmuhammadi]

Great Explanation! Thanks :)

[@kristakingmath]

Thanks Aman!

[@yogendravishwakarma5592]

Very nice and conceptual explanation mam thanks a lot.

[@kristakingmath]

You're welcome, Yogendra! I'm so glad it helped! :)

[@abhishekkashyap1764]

An interesting video this was.

[@greta1114]

bestie krista ily

[@ripunjayvishwakarma2275]

wow more helpful for me....nd nice learning way

[@kristakingmath]

I'm so glad it helped!

[@lisazhang7369]

How do I type inverse tan, sec, and cosec into a ti36 calculator?

[@Hasko-j9t]

very usefu. Thank you so much.

[@kristakingmath]

I'm glad it could help!

[@skyskraypa88]

Question. What about setting the arctan equal to x makes you come up with pi/4 or pi/2 ? Besides the math of course.

[@veritasiumaequitasius3530]

The math. I'm not sure what else you could mean. Look at the "unit circle" of trigonometry

[@Ayayron_e3]

about 3 weeks late haha.. but no worries - just passed college calc 2 with a B so i'm happy :) I didn't like to study :/

[@kristakingmath]

+aaron brooks Congratulations on passing, that's awesome! Enjoy your summer! :)

[@namrathareddy8176]

krista u r superb nice video

[@kristakingmath]

Thank you so much!

[@sharonsolana]

💙 L O V E T H E V I D E O ! T H A N K Y O U !

[@Awesome1096]

Couldn't this be made easier with a basic comparison test first with 1/n² which is clearly larger then 1/(n²+1) since all its terms are larger so we could then apply the integral test on that which is a much simpler integral it's just 1/3 this showing the smaller series converges

[@sharonsolana]

🍎 F O R T H E T E A C H E R ! 🍏

[@kristakingmath]

Thanks, Sharon!

[@sharonsolana]

✩ ✫ ✬ ✮ ✯ !

[@mitch_comer]

why are you the only one she lkes?

[@mjl7810]

Still so confusing..

[@nebiyuwalelign9383]

Krisa thinks

[@kristakingmath]

You're welcome!

[@meshalwanigaming2702]

fuck this im dropping out

[@meshalwanigaming2702]

Thank you for the video tho