Improper Integrals - Convergent or Divergent (Made Easy)
HTML-код
- Опубликовано: 6 сен 2024
- In this video, I will show you how to evaluate an improper integral and determine if it is convergent or divergent. This is a lesson made easy for Calculus students. An integral is improper if there is an infinity sign on the top or bottom of the integral. An integral is also improper if there exists a value between the the upper and lower limit of an integral such that the function will be divide-by-zero. I will show some easy examples in the video.
The general way to solve an improper integral and determine their convergence or divergence in Calculus is to turn it into a limit as t approaches infinity. Then, you use the first fundamental theorem of calculus or the second fundamental theorem of calculus to evaluate the integral like you normally do. It also involves finding the antiderivative of the integral and plugging the limits in.
In the next video, I will show you how to evaluate integrals and determine if they are convergent or divergent using the Comparison Test for Improper Integrals.
LIKE & SUBSCRIBE:
🔴 My Channel: / quocdatphung
🔴 My second channel: / @purifynature8479
MY EQUIPMENT:
✅Camera: Samsung Galaxy J7
✅Recording Equipment: obsproject.com/
✅Editing Software: Shotcut
I need my calculus 2 class to get into my degree and I have been struggling a lot. This finally is starting to make sense. Thank you so much for this video and for your channel in general.
I'm very glad that it's useful to you! I hope you'd subscribe (it means a lot hehe). You can find all of my Calculus 2 videos here: ruclips.net/p/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA
Love from India❤❤
Its helpful for my maths(abstract algebra) exam❤❤
You're very welcome Virendralakhawat! Please don't forget to share with your classmates and kindly subscribe ~ you can find all of my Calculus II videos in this link: ruclips.net/p/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA
5:23 and 6:36 LIATE = Logs Inverse Trig m, Algebra, Trig Exponential for Integration by Parts ie uv-vdu
That's right! If you like my Calculus II videos, you can find the rest of them here: ruclips.net/p/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA
I go to uoft and you explain sooo well bro
Thanks AnonymousAdeptt! I go to UOttawa :) Please don't forget to share with your classmates and kindly subscribe ~ all of my Calculus II videos in this link: ruclips.net/p/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA
You do a better job than my teacher and any math video on RUclips. This video will really help me to prepare for my exam. Thank you.
Thanks so much Justin! If you really like my videos, please kindly subscribe, it means so much! As well, good luck on your exam! Here's the rest of my Calculus 2 videos in this playlist: ruclips.net/p/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA
Amazing video!!! Perfect and detailed explanation!!! Really the perfect video that makes you enjoy maths!!!🥳🥳🤗😊
Thanks Jonny! When you take Calculus II, you can find all of my videos for that course here: ruclips.net/p/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA
I don't know why you have low subscription because the way you teach it's amazing...thank you
Haha thank you so much! Please share with your classmates if they need any help. As well, you can find all of my Calculus II videos in this link: ruclips.net/p/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA
🎈🎈🎈 awesome ... solving integrals is so much fun 🎈🎈🎈
Thank you so much @Silent Integrals! I have already subscribed to your channel! Don't forget to subscribe mine to support me too!
i did really give you a good clap after watching the video thankssss😭. saved my life
You're very welcome Korodeferanmi! I have many more Calculus II walkthroughs! You can find them all here: ruclips.net/p/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA
Thank you this video was super helpful. My professor never explained properly what to make u and du even though I've asked him many times. Finally, with this video I understand.
You're welcome Baloney! You can find all of my Calculus videos in this link: ruclips.net/p/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA
I AM STARTING TO LOVE MATH BECAUSE OF YOU. Thank you so much. ❤
I'm so happy to hear that Enid! Please kindly subscribe and share with your friends my Calculus playlist: ruclips.net/p/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA
Omg this video is perrrfect
Thanks so much Nazlk! You can find all of my Calculus II videos in the following link (don't forget to share with your classmates and kindly subscribe too!): ruclips.net/p/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA
Hi
I am from India and I watch your video for first time
It's fantastic 😍😍
Hi Ska! I'm really happy that you like it! You can find all of my Calculus II videos in this link (don't forget to share and kindly subscribe too!): ruclips.net/p/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA
For the last problem, why did you split it as you didn't do so for the previous problem.
There's a vertical asymptote at x=1 for the last problem (meaning when x=1 it's divide by 0). So you have to split it. :) Let me know if that makes sense. If you don't split you're gonna get weird and incorrect results because it's divide by 0.
@@QuocDatPhungthank you for your response! if that’s the case then why not split the 2nd problem as the denominator is gonna be zero as well?
@@user-cp1lo8sn9u For the second problem, the denominator is zero when x =0, but we are integrating from x=1 to x=infinity. If divide by 0 doesn't occur when we integrate from x=a to x=b then we don't need to split. If it occurs, then we have to split it (as seen in the last problem, divide by 0 happens when x =1 and we are integrating from x=0 to x=3). Let me know if that makes sense!
@@QuocDatPhung ohhh ok, i understand now. Thank you so much!
@@user-cp1lo8sn9uNo worries! You can find all of my Calculus II tutorials in this playlist: ruclips.net/p/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA
This video is amazing thank you very much you are concise and straight to the point thank you so much this was really helpful !!!
Thanks so much Caurt! I'm glad you like them! You can find all of my Calculus II videos here: ruclips.net/p/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA
Hello sir Have u teached the Gamma,beta and alpha function of improper integrals...?? If yes would love you to show the playlist thanks..
Hi Anshumansahu! I will keep working on new math topics. For now, you can find all of my Calculus 2 videos in this playlist here: ruclips.net/p/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA
Hi there :)
For the final question (20:22) why did you say the limit as t approaches 1 from the negative side? why not the positive side?
If you graph 1/(x-1), you see that there is a vertical asymptote at x=1. The integral goes from 0 to 1 right? We are approaching 1 from the left. So, this is equivalent with saying the "limit as t approaches 1 from the negative side", meaning from the left side. Let me know if that makes sense.
@@QuocDatPhung Thank you :)
Awesome 💯
Thank you KamanziRayan!! I'm really glad you enjoyed my video! I would really appreciate if you could share with your classmates or kindly subscribe ~ you can find all of my Calculus II videos in this link: ruclips.net/p/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA
i feel like im gonna fail tomorrow to be honest
You're not going to fail! If you need help you can find all of my Calculus II videos in this link: ruclips.net/p/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA
How did it go? Mine's tomorrow💀
@@Heelo_0 Good luck!
@QuocDatPhung thanks brother, take care
Any updates? How did it go for y'all 💀
Thanks I really appreciate it. I was struggling with this topic however I am getting it better now thanks to this video.
You're very welcome Jaden! Since you're taking Calculus II, you can find all of my videos for that course here: ruclips.net/p/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA
Great video, super helpful for for my calc final tommorow, GO RAVENS haha.
Good luck! Please kindly subscribe and share! You can also find the rest of my Calculus II videos here: ruclips.net/p/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA
I really like how you explain the pitfalls too
Thanks Sarah! You can find all of my Calculus II videos in this playlist: ruclips.net/p/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA
your the man Mr. Phung
I have a question, why did we split the last integral into two, but not the second to last? Since they both have bounds that are "regular" numbers.
Good question! For the last question (lower bound of 0 and upper bound of 3), there is a vertical asymptote at x=1 (because when x=1, the you get division by 0). If the asymptote is in between the bounds, you have to split the integral. As for the second to last question (lower bound of 2 and upper bound of 5), the vertical asymptote is at x=2. Since it's technically not in between the bounds, you don't have to split it. Please let me know if this makes sense!
@@QuocDatPhung Makes perfect sense thank you for answering!
I want to know, is there another way to know on how to know which to put 2+/2- other than using graph😢
Hi please let me know the timestamp in the video so I know which problem you're referring to :))
thank you so much!! this helped me a lot!!
You're so welcome Malaika! Please kindly subscribe and share my RUclips Calculus course here: ruclips.net/p/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA
This was so helpful. Thank you so much sir you really helped me understand this concept!!!!
Thank you for your kind words Marty! If you like my videos please don't forget to subscribe and share with your classmates. I want to help them learn math too!
Thank you for assistance my Gee
You're very welcome! If you enjoy my content, you can find the rest of my Calculus 2 videos here: ruclips.net/p/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA
we love u man
Thank you Idunno! Please kindly share and subscribe (it means a lot) you can find all of my Calculus II videos in this link: ruclips.net/p/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA
I just subscribed!
you're great at explaining! thank you for the video.
WOW thanks a million Emyr! You can find all of my Calculus 2 videos in the following playlist:ruclips.net/p/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA And please also share with your classmates if you find these helpful too!
@@QuocDatPhung You're welcome! I just did !
Please consider doing a video on langrage multipliers, multiple integrals and matrices, maxima minima later! I'm preparing for my midterms now but I'll have my finals later :D
thank you again ;)
@@emyrgrznsky9943 Thanks for letting me know! Good luck!
thanks for the great practice problems!
You're welcome :D! You can find all of my Calculus II videos here: ruclips.net/p/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA
Thank you, you made it really simple
I'm glad it helped, Will! Please kindly subscribe and you can find the rest of my Calculus 2 videos here: ruclips.net/p/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA
at 20:00 why did u split it from 0 to 1 and 1 to 3. How did u know to pick these numbers?
Hello! Notice how the denominator is 0 when x = 1. Therefore, we have to split the integral, 0 to 1, and 1 to 3. Please let me know if that makes sense!
thank you so much @@QuocDatPhung
Thank you so much
You're welcome! I'm glad you like it! You can find the rest of my Calculus videos in this playlist: ruclips.net/p/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA
on par with the indian guy teaching on youtube 🙏
Thanks a lot Ewgna! If you like my Calculus II videos, you can find all of them together in this link: ruclips.net/p/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA
You’re the best
Thanks Dani! Please kindly subscribe and share with your classmates my Calculus playlist: ruclips.net/p/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA
THANK YOUUUU!
You're very welcome! I have other Calculus II videos too! You can find all of my Calculus II videos here: ruclips.net/p/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA
God bless u
Thank you Tumim! Please hit the subscribe button and share with your classmates. As well, you can find all of my Calculus videos here: ruclips.net/p/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA
afuuftuu bareechii ibsi
Thank you! Please subscribe and share :)
Can you add more examples please
Hi Mafo! I have another video of improper integrals in this playlist in the following link (scroll down and see the video right after this one. Please let me know if you found it) ruclips.net/p/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA
Or just go into the playlist link and hit Ctr+F for "Improper Integrals" and then you will see my other video. Keep this playlist as it has all the Calculus videos in it.
thank yours helpful
You're welcome! You can find all of my Calculus II videos here: ruclips.net/p/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA
thanks
You're very welcome Vinh Khang! If you want to see more of my Calculus videos, you can find all of them here: ruclips.net/p/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA
Hết xảy!
Cám ơn bạn! Bạn có thể tìm tất cả clip của mình về Calculus 2 ở đây: ruclips.net/p/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA
How tf are we supposed to know what the graph of e^t looks like to know it approaches 0?? Or the graphs of any of the other functions. Fuck math and fuck universities.
Remember exponential functions, like e^x from high school? when you graph y=e^x, you know when x=0, y=1. Therefore, the graph of e^t approaches 1 when t is near 0.
great great great video, thank you so much
Thanks so much Elsa! You can find all of my Calculus II videos in the following link (don't forget to share and kindly subscribe!): ruclips.net/p/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA