Improper Integrals - Convergent or Divergent (Made Easy)

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  • 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.
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Комментарии • 108

  • @jaime.dragon
    @jaime.dragon 7 месяцев назад +22

    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.

    • @QuocDatPhung
      @QuocDatPhung  7 месяцев назад +3

      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

  • @virendralakhawat1087
    @virendralakhawat1087 3 месяца назад +4

    Love from India❤❤
    Its helpful for my maths(abstract algebra) exam❤❤

    • @QuocDatPhung
      @QuocDatPhung  3 месяца назад +2

      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

  • @user-xl1ig1bn6i
    @user-xl1ig1bn6i 9 месяцев назад +2

    5:23 and 6:36 LIATE = Logs Inverse Trig m, Algebra, Trig Exponential for Integration by Parts ie uv-vdu

    • @QuocDatPhung
      @QuocDatPhung  9 месяцев назад +1

      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

  • @AnonymousAdeptt
    @AnonymousAdeptt 2 месяца назад +2

    I go to uoft and you explain sooo well bro

    • @QuocDatPhung
      @QuocDatPhung  2 месяца назад +1

      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

  • @justinmedia1621
    @justinmedia1621 Год назад +5

    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.

    • @QuocDatPhung
      @QuocDatPhung  Год назад +2

      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

  • @JonnyMath
    @JonnyMath 10 месяцев назад +8

    Amazing video!!! Perfect and detailed explanation!!! Really the perfect video that makes you enjoy maths!!!🥳🥳🤗😊

    • @QuocDatPhung
      @QuocDatPhung  10 месяцев назад +2

      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

  • @kwetsimajunior8532
    @kwetsimajunior8532 11 месяцев назад +2

    I don't know why you have low subscription because the way you teach it's amazing...thank you

    • @QuocDatPhung
      @QuocDatPhung  11 месяцев назад +2

      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

  • @silentintegrals9104
    @silentintegrals9104 2 года назад +14

    🎈🎈🎈 awesome ... solving integrals is so much fun 🎈🎈🎈

    • @QuocDatPhung
      @QuocDatPhung  2 года назад +7

      Thank you so much @Silent Integrals! I have already subscribed to your channel! Don't forget to subscribe mine to support me too!

  • @korodeferanmi8338
    @korodeferanmi8338 6 месяцев назад +2

    i did really give you a good clap after watching the video thankssss😭. saved my life

    • @QuocDatPhung
      @QuocDatPhung  6 месяцев назад +1

      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

  • @baloneypopo9609
    @baloneypopo9609 9 месяцев назад +1

    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.

    • @QuocDatPhung
      @QuocDatPhung  9 месяцев назад +1

      You're welcome Baloney! You can find all of my Calculus videos in this link: ruclips.net/p/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA

  • @enidfrommyname
    @enidfrommyname Год назад +3

    I AM STARTING TO LOVE MATH BECAUSE OF YOU. Thank you so much. ❤

    • @QuocDatPhung
      @QuocDatPhung  Год назад +1

      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

  • @nazlk.5933
    @nazlk.5933 5 месяцев назад +2

    Omg this video is perrrfect

    • @QuocDatPhung
      @QuocDatPhung  5 месяцев назад +1

      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

  • @SKa397
    @SKa397 5 месяцев назад +1

    Hi
    I am from India and I watch your video for first time
    It's fantastic 😍😍

    • @QuocDatPhung
      @QuocDatPhung  5 месяцев назад +1

      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

  • @user-cp1lo8sn9u
    @user-cp1lo8sn9u 5 месяцев назад +1

    For the last problem, why did you split it as you didn't do so for the previous problem.

    • @QuocDatPhung
      @QuocDatPhung  5 месяцев назад +1

      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.

    • @user-cp1lo8sn9u
      @user-cp1lo8sn9u 5 месяцев назад +1

      @@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?

    • @QuocDatPhung
      @QuocDatPhung  5 месяцев назад +1

      @@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!

    • @user-cp1lo8sn9u
      @user-cp1lo8sn9u 5 месяцев назад +1

      @@QuocDatPhung ohhh ok, i understand now. Thank you so much!

    • @QuocDatPhung
      @QuocDatPhung  5 месяцев назад +1

      @@user-cp1lo8sn9uNo worries! You can find all of my Calculus II tutorials in this playlist: ruclips.net/p/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA

  • @Caurt.
    @Caurt. 10 месяцев назад +4

    This video is amazing thank you very much you are concise and straight to the point thank you so much this was really helpful !!!

    • @QuocDatPhung
      @QuocDatPhung  10 месяцев назад +2

      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

  • @Anshumansahu23
    @Anshumansahu23 9 месяцев назад +2

    Hello sir Have u teached the Gamma,beta and alpha function of improper integrals...?? If yes would love you to show the playlist thanks..

    • @QuocDatPhung
      @QuocDatPhung  9 месяцев назад +1

      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

  • @matricmasterclass4245
    @matricmasterclass4245 9 месяцев назад +2

    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?

    • @QuocDatPhung
      @QuocDatPhung  9 месяцев назад +2

      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.

    • @matricmasterclass4245
      @matricmasterclass4245 9 месяцев назад

      @@QuocDatPhung Thank you :)

  • @KamanziRayan-oz3qw
    @KamanziRayan-oz3qw 4 месяца назад +2

    Awesome 💯

    • @QuocDatPhung
      @QuocDatPhung  4 месяца назад +2

      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

  • @Valecia306
    @Valecia306 3 месяца назад +15

    i feel like im gonna fail tomorrow to be honest

    • @QuocDatPhung
      @QuocDatPhung  3 месяца назад +1

      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

    • @Heelo_0
      @Heelo_0 2 месяца назад +2

      How did it go? Mine's tomorrow💀

    • @QuocDatPhung
      @QuocDatPhung  2 месяца назад +1

      @@Heelo_0 Good luck!

    • @Heelo_0
      @Heelo_0 2 месяца назад

      @QuocDatPhung thanks brother, take care

    • @AnonymousAlien2099
      @AnonymousAlien2099 2 месяца назад

      Any updates? How did it go for y'all 💀

  • @jadendodoo4979
    @jadendodoo4979 10 месяцев назад +1

    Thanks I really appreciate it. I was struggling with this topic however I am getting it better now thanks to this video.

    • @QuocDatPhung
      @QuocDatPhung  10 месяцев назад +1

      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

  • @Clipaholick
    @Clipaholick 8 месяцев назад +1

    Great video, super helpful for for my calc final tommorow, GO RAVENS haha.

    • @QuocDatPhung
      @QuocDatPhung  8 месяцев назад +1

      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

  • @sarahchasauce935
    @sarahchasauce935 9 месяцев назад

    I really like how you explain the pitfalls too

    • @QuocDatPhung
      @QuocDatPhung  9 месяцев назад

      Thanks Sarah! You can find all of my Calculus II videos in this playlist: ruclips.net/p/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA

  • @user-bt8nh4ou1p
    @user-bt8nh4ou1p 6 месяцев назад +1

    your the man Mr. Phung

  • @Boole262
    @Boole262 Год назад +1

    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.

    • @QuocDatPhung
      @QuocDatPhung  Год назад +2

      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!

    • @Boole262
      @Boole262 Год назад

      @@QuocDatPhung Makes perfect sense thank you for answering!

  • @ayuniamira3425
    @ayuniamira3425 7 месяцев назад +1

    I want to know, is there another way to know on how to know which to put 2+/2- other than using graph😢

    • @QuocDatPhung
      @QuocDatPhung  7 месяцев назад +1

      Hi please let me know the timestamp in the video so I know which problem you're referring to :))

  • @malaika9352
    @malaika9352 Год назад +2

    thank you so much!! this helped me a lot!!

    • @QuocDatPhung
      @QuocDatPhung  Год назад +1

      You're so welcome Malaika! Please kindly subscribe and share my RUclips Calculus course here: ruclips.net/p/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA

  • @marty5585
    @marty5585 2 года назад +4

    This was so helpful. Thank you so much sir you really helped me understand this concept!!!!

    • @QuocDatPhung
      @QuocDatPhung  2 года назад +3

      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!

  • @lasarusindongo7741
    @lasarusindongo7741 Год назад +2

    Thank you for assistance my Gee

    • @QuocDatPhung
      @QuocDatPhung  Год назад +1

      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

  • @idunnoanymore2814
    @idunnoanymore2814 19 дней назад +1

    we love u man

    • @QuocDatPhung
      @QuocDatPhung  День назад +1

      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

  • @emyrgrznsky9943
    @emyrgrznsky9943 Год назад +3

    I just subscribed!
    you're great at explaining! thank you for the video.

    • @QuocDatPhung
      @QuocDatPhung  Год назад +4

      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!

    • @emyrgrznsky9943
      @emyrgrznsky9943 Год назад +4

      @@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 ;)

    • @QuocDatPhung
      @QuocDatPhung  Год назад +4

      @@emyrgrznsky9943 Thanks for letting me know! Good luck!

  • @sydneylee823
    @sydneylee823 9 месяцев назад +1

    thanks for the great practice problems!

    • @QuocDatPhung
      @QuocDatPhung  9 месяцев назад +1

      You're welcome :D! You can find all of my Calculus II videos here: ruclips.net/p/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA

  • @will9678
    @will9678 Год назад +1

    Thank you, you made it really simple

    • @QuocDatPhung
      @QuocDatPhung  Год назад +1

      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

  • @aslancemtokbas8472
    @aslancemtokbas8472 11 месяцев назад +1

    at 20:00 why did u split it from 0 to 1 and 1 to 3. How did u know to pick these numbers?

    • @QuocDatPhung
      @QuocDatPhung  11 месяцев назад +2

      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!

    • @aslancemtokbas8472
      @aslancemtokbas8472 11 месяцев назад +1

      thank you so much @@QuocDatPhung

  • @duniasy
    @duniasy 8 месяцев назад +1

    Thank you so much

    • @QuocDatPhung
      @QuocDatPhung  8 месяцев назад +1

      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

  • @ewgna1014
    @ewgna1014 10 месяцев назад +1

    on par with the indian guy teaching on youtube 🙏

    • @QuocDatPhung
      @QuocDatPhung  10 месяцев назад +1

      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

  • @DANIFUTUREMD
    @DANIFUTUREMD Год назад +1

    You’re the best

    • @QuocDatPhung
      @QuocDatPhung  Год назад +1

      Thanks Dani! Please kindly subscribe and share with your classmates my Calculus playlist: ruclips.net/p/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA

  • @abigailmathew2498
    @abigailmathew2498 6 месяцев назад +1

    THANK YOUUUU!

    • @QuocDatPhung
      @QuocDatPhung  6 месяцев назад +1

      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

  • @tumimtaye8939
    @tumimtaye8939 Год назад +3

    God bless u

    • @QuocDatPhung
      @QuocDatPhung  Год назад +2

      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

  • @MelkamuEndeshaw
    @MelkamuEndeshaw Год назад +2

    afuuftuu bareechii ibsi

    • @QuocDatPhung
      @QuocDatPhung  Год назад +2

      Thank you! Please subscribe and share :)

  • @mafoitamba7599
    @mafoitamba7599 Год назад +2

    Can you add more examples please

    • @QuocDatPhung
      @QuocDatPhung  Год назад +2

      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

    • @QuocDatPhung
      @QuocDatPhung  Год назад +2

      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.

  • @user-xf6mt2ee4j
    @user-xf6mt2ee4j 9 месяцев назад +1

    thank yours helpful

    • @QuocDatPhung
      @QuocDatPhung  9 месяцев назад +1

      You're welcome! You can find all of my Calculus II videos here: ruclips.net/p/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA

  • @-VinhKhang_yearsago
    @-VinhKhang_yearsago 10 месяцев назад +1

    thanks

    • @QuocDatPhung
      @QuocDatPhung  10 месяцев назад +1

      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

  • @thomasblackwell9507
    @thomasblackwell9507 Год назад

    Hết xảy!

    • @QuocDatPhung
      @QuocDatPhung  Год назад

      Cám ơn bạn! Bạn có thể tìm tất cả clip của mình về Calculus 2 ở đây: ruclips.net/p/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA

  • @Burningarrow7
    @Burningarrow7 7 месяцев назад +1

    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.

    • @QuocDatPhung
      @QuocDatPhung  7 месяцев назад +1

      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.

  • @nutritionbyelsa
    @nutritionbyelsa 5 месяцев назад +1

    great great great video, thank you so much

    • @QuocDatPhung
      @QuocDatPhung  5 месяцев назад +1

      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