Comparison Test for Improper Integrals

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  • เผยแพร่เมื่อ 25 ม.ค. 2025

ความคิดเห็น • 115

  • @AndreaFerro-ks6bp
    @AndreaFerro-ks6bp ปีที่แล้ว +8

    No words, you are the best as always!!

    • @QuocDatPhung
      @QuocDatPhung  ปีที่แล้ว +1

      Wow, thank you Andrea! If you really like my Calculus 2 videos, you can find the rest of them in this playlist: th-cam.com/play/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA.html

  • @voltaire8828
    @voltaire8828 ปีที่แล้ว +4

    We love you Dat, cant imagine life without you

    • @QuocDatPhung
      @QuocDatPhung  ปีที่แล้ว +1

      You're welcome! I'm glad you like it! You can find the rest of my Calculus videos in this playlist: th-cam.com/play/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA.html

  • @nutritionbyelsa
    @nutritionbyelsa 10 หลายเดือนก่อน +4

    epic resource, thank you so much, so hard to find high quality resources on advanced math topics, sharing with my calc class at UBC, thank you : )

    • @QuocDatPhung
      @QuocDatPhung  10 หลายเดือนก่อน +1

      Thanks so much! I really appreciate it!!!

    • @rainymc
      @rainymc 10 หลายเดือนก่อน +1

      omg hi i saw your piazza post! thanks so much for sharing this vid!!!

    • @QuocDatPhung
      @QuocDatPhung  10 หลายเดือนก่อน +2

      @@rainymc You're very welcome! I don't have just this video, I have an entire playlist for Calculus II :) th-cam.com/play/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA.html

  • @yonghoon8805
    @yonghoon8805 ปีที่แล้ว +11

    Thank you! Your videos are very helpful and you explain all that complicated math with a smile on your face, amazing!

    • @QuocDatPhung
      @QuocDatPhung  ปีที่แล้ว +1

      Thank you very much Yonghoon! I'm glad you enjoy it! You can find all of my Calculus 2 videos in this playlist: th-cam.com/play/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA.html

  • @NCont-i7g
    @NCont-i7g 10 หลายเดือนก่อน +4

    Truly appreciate those extra problems!

  • @KHOATRANANH-po5pv
    @KHOATRANANH-po5pv 7 หลายเดือนก่อน +1

    anh giảng hay quá, anh nói tiếng anh dễ nghe mà chuẩn. Mong anh sản xuất thêm nhiều video hay và chất lượng nữa ạ.

    • @QuocDatPhung
      @QuocDatPhung  7 หลายเดือนก่อน +1

      Cám ơn em! Em nhớ chia sẽ cho các bạn học và đăng kí ủng hộ anh nhé. Những bài dạy toán của anh ở đây: th-cam.com/play/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA.html

  • @hemberry_
    @hemberry_ 2 หลายเดือนก่อน +2

    really helpful to sit down and solve some integrals with someone when you have a double degree and have to manage your time independently!!

    • @QuocDatPhung
      @QuocDatPhung  2 หลายเดือนก่อน +1

      That’s awesome! Glad my videos are helping! What are your double degrees in, if I may ask?

    • @hemberry_
      @hemberry_ 2 หลายเดือนก่อน +1

      @@QuocDatPhung I’m in a weird system where you have to have a double degree to apply for med school. it’s kinda horrible; i chose maths, but as I didn’t pass last year, the maths part has gotten really hard to manage (I can’t afford spending lots of time on it because I’m preparing my contest). so yeah, I hope to pass in med school this year…

    • @QuocDatPhung
      @QuocDatPhung  2 หลายเดือนก่อน +1

      @@hemberry_ That sounds tough. I wish you the best of luck!

  • @vivienshaanika
    @vivienshaanika ปีที่แล้ว +6

    You are a good tutor, this is amazing and continue doing your best 🙌🙌👏👏👏

    • @QuocDatPhung
      @QuocDatPhung  ปีที่แล้ว +1

      Hi Vivien! Thank you so much! Please kindly subscribe and share with your classmates. You can find all of my Calculus II videos here: th-cam.com/play/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA.html

  • @嘉元张-y4f
    @嘉元张-y4f 10 หลายเดือนก่อน +4

    Best youtube teacher

    • @QuocDatPhung
      @QuocDatPhung  10 หลายเดือนก่อน +1

      Thank you! You can find all of my Calculus II videos in this playlist here: th-cam.com/play/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA.html

  • @sa_0515
    @sa_0515 4 หลายเดือนก่อน +1

    Greetings from the University of Florida. Have a Midterm in Calc 2 in 2 days 😅 Thank you a lot

    • @QuocDatPhung
      @QuocDatPhung  4 หลายเดือนก่อน

      Thank you Sa0515! I'm glad you found my videos helpful! Please kindly share with your classmates to help them and subscribe to support me (it means a lot). As well, you can find all of my Calculus II videos in this link: th-cam.com/play/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA.html

  • @mertyilmaz2442
    @mertyilmaz2442 2 ปีที่แล้ว +8

    Awesome as always :)

    • @QuocDatPhung
      @QuocDatPhung  2 ปีที่แล้ว +5

      Thank you for your kind words Mert! :))))

  • @sahilbhagat7206
    @sahilbhagat7206 ปีที่แล้ว +3

    Thank you very much to clearing concepts so easily.

    • @QuocDatPhung
      @QuocDatPhung  ปีที่แล้ว +2

      Thanks so much Sahilbhagat! Please kindly subscribe and share with your classmates. You can find all of my Calculus II videos here: th-cam.com/play/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA.html

  • @bossbabe6064
    @bossbabe6064 ปีที่แล้ว +5

    Hi, thank you for this video! I have just one question, how do you determine the function g(x)? How do I know which function to use to compare to f(x)?

    • @QuocDatPhung
      @QuocDatPhung  ปีที่แล้ว +5

      You can use this list (order from smallest to largest) to pick your g(x), but it does take a bit of practice to figure it out:
      constant < log(x) < sqrt(x) < x < xlogx < polynomial < exponential < factorial

    • @QuocDatPhung
      @QuocDatPhung  ปีที่แล้ว +3

      You can also see all of my Calculus II videos in this playlist: th-cam.com/play/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA.html

  • @tailingoff
    @tailingoff ปีที่แล้ว +1

    Thanks for showing the counter example and also letting me know that hit and trial is the way we approach these tests. 😊

    • @QuocDatPhung
      @QuocDatPhung  ปีที่แล้ว +1

      You're very welcome! If you like my Calculus videos, you can find the rest of them here: th-cam.com/play/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA.html

  • @mrmansir3734
    @mrmansir3734 6 หลายเดือนก่อน +1

    very well made videos. I liked your improper integral video too

    • @QuocDatPhung
      @QuocDatPhung  6 หลายเดือนก่อน +1

      Thanks Mr.Mansir! Please don't forget to share with your classmates and kindly subscribe ~ you can find all of my Calculus II videos in this link: th-cam.com/play/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA.html

  • @chic9205
    @chic9205 หลายเดือนก่อน +1

    Thank you, my hero!

    • @QuocDatPhung
      @QuocDatPhung  16 วันที่ผ่านมา +2

      You're welcome Chic! I'm really glad you like my explanation! If you know anyone who needs help with this class, please kindly share with them and also subscribe to support me (it means a lot) ~ you can find all of my Calculus 2 videos in this link: th-cam.com/play/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA.html

  • @bilgexo5973
    @bilgexo5973 2 ปีที่แล้ว +2

    i hope you live happily forever. thank u for the video

    • @QuocDatPhung
      @QuocDatPhung  2 ปีที่แล้ว +2

      Thank you and you too! Please don't forget to subscribe and share my calculus playlist with your classmates! th-cam.com/play/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA.html

  • @Evelyn-oy8li
    @Evelyn-oy8li ปีที่แล้ว +1

    Thank you so much, finally i could understand this topic after confusing during class. Thankyou 🥺🥺🥺

    • @QuocDatPhung
      @QuocDatPhung  ปีที่แล้ว +1

      Thanks so much! Please kindly subscribe! Also, you can find the rest of my Calculus videos here: th-cam.com/play/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA.html

  • @ldhung308
    @ldhung308 8 หลายเดือนก่อน +2

    cảm ơn thầy vì bài giảng hữu ích

    • @QuocDatPhung
      @QuocDatPhung  8 หลายเดือนก่อน +2

      Cám ơn em! Em chia sẻ với các bạn khác học nhé.

  • @na.1221
    @na.1221 2 ปีที่แล้ว +8

    Thanks teacher please keep it up

    • @QuocDatPhung
      @QuocDatPhung  2 ปีที่แล้ว +6

      Thank you for your kind words Nardos!

    • @na.1221
      @na.1221 2 ปีที่แล้ว +5

      No problem but can you work English grammatical for e.g relative clause and relative pronoun

    • @QuocDatPhung
      @QuocDatPhung  2 ปีที่แล้ว +5

      @@na.1221 That's a good idea Nardos! I am planning to make videos on English grammar in the future too! Stay tuned!

    • @na.1221
      @na.1221 2 ปีที่แล้ว +4

      Ok i will expect

    • @QuocDatPhung
      @QuocDatPhung  2 ปีที่แล้ว +4

      @@na.1221 Awesome!

  • @Eagle._._.
    @Eagle._._. 2 ปีที่แล้ว +4

    Thank you for saving my life

    • @QuocDatPhung
      @QuocDatPhung  2 ปีที่แล้ว +3

      Thanks Eagle! If you enjoyed my clip, please do hit that subscribe button and share with classmates. As well, you can find the rest of my Calculus videos in this playlist: th-cam.com/play/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA.html

  • @gaming3rbbi393
    @gaming3rbbi393 7 หลายเดือนก่อน +1

    لك بتشرح احسن من العرب

    • @QuocDatPhung
      @QuocDatPhung  7 หลายเดือนก่อน +1

      Thank you! Please don't forget to share with your classmates and kindly subscribe ~ you can find all of my Calculus II videos in this link: th-cam.com/play/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA.html

  • @reemsayed9671
    @reemsayed9671 2 ปีที่แล้ว +3

    You are so great may God bless you 💜

    • @QuocDatPhung
      @QuocDatPhung  2 ปีที่แล้ว +3

      Thank you so much! You are awesome too! Please don't forget to subscribe and share my Calculus playlist here: th-cam.com/play/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA.html

  • @bhtkyav7420
    @bhtkyav7420 11 หลายเดือนก่อน +2

    thank youuu everything is clear noww :)

    • @QuocDatPhung
      @QuocDatPhung  11 หลายเดือนก่อน +1

      That's great! You can find all of my Calculus II videos here: th-cam.com/play/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA.html

  • @emberlynnguyen3458
    @emberlynnguyen3458 ปีที่แล้ว +3

    Your explanations are really comprehensible! Thank you so much!

    • @QuocDatPhung
      @QuocDatPhung  ปีที่แล้ว +1

      Thanks so much Emberlyn! You can find the rest of my calculus videos in this playlist here (please kindly subscribe and share also!) :th-cam.com/play/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA.html

  • @HanifaNasala
    @HanifaNasala 8 หลายเดือนก่อน +1

    Thank you, it's very easy to follow and understand😊

    • @QuocDatPhung
      @QuocDatPhung  8 หลายเดือนก่อน +1

      You're very welcome! Please don't forget to share with your classmates and kindly subscribe ~ you can find all of my Calculus II videos in this link: th-cam.com/play/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA.html

  • @matthewwaite2679
    @matthewwaite2679 2 ปีที่แล้ว +3

    Clear and concise!

    • @QuocDatPhung
      @QuocDatPhung  2 ปีที่แล้ว +2

      Thank you Matthew! Good luck on your tests!

  • @AungKhantPaing-q9q
    @AungKhantPaing-q9q ปีที่แล้ว +2

    I am loving you so much!

    • @QuocDatPhung
      @QuocDatPhung  ปีที่แล้ว +1

      Thanks a lot! Please kindly subscribe and share! Also, you can find all of my Calculus II videos here: th-cam.com/play/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA.html

  • @ibrahimtunahandag6081
    @ibrahimtunahandag6081 ปีที่แล้ว +2

    Bro why did u do that! Why did you split it from 1?

    • @QuocDatPhung
      @QuocDatPhung  ปีที่แล้ว +1

      Which problem are you referring to? Please give me the timestamp. I have to split it if there is a vertical asymptote at x=1

    • @ibrahimtunahandag6081
      @ibrahimtunahandag6081 ปีที่แล้ว +1

      first one@@QuocDatPhung

    • @ibrahimtunahandag6081
      @ibrahimtunahandag6081 ปีที่แล้ว

      like...are we always choosing 1 as a start point?@@QuocDatPhung

    • @QuocDatPhung
      @QuocDatPhung  ปีที่แล้ว +1

      @@ibrahimtunahandag6081 I see. You mean the problem at 1:34. This integral goes from 0 to infinity. Now, if you look at the top right corner of the video, the first step is to make sure that the integral goes from 1 to infinity (that's just the way they want you to do it). Since the integral is from 0 to infinity, then we split it into two integrals, one going from 0 to 1, and the other going from 1 to infinity. Let me know if that makes sense.

    • @ibrahimtunahandag6081
      @ibrahimtunahandag6081 ปีที่แล้ว +1

      @@QuocDatPhung so we basically choose 1. But why not 2, 3, 4 or e?

  • @ssamirs1881
    @ssamirs1881 ปีที่แล้ว +2

    What happens if the numerator is not always positive?

    • @QuocDatPhung
      @QuocDatPhung  ปีที่แล้ว +1

      You can factor out the -1 and move it outside the integral, since it is a constant.

    • @ssamirs1881
      @ssamirs1881 ปีที่แล้ว +1

      @@QuocDatPhung No, I mean for the second step, like for example a sin(x).

    • @QuocDatPhung
      @QuocDatPhung  ปีที่แล้ว +1

      @@ssamirs1881 In the description of a video, I attached a Google Drive link that contains an example of cos(x) on the numerator (on the last page). Let me know if that helps.

    • @QuocDatPhung
      @QuocDatPhung  ปีที่แล้ว +1

      @@ssamirs1881 Oh I meant the description of this video. Let me know if you can find it.

  • @THEoneandonlystika
    @THEoneandonlystika 10 หลายเดือนก่อน +2

    nice one

    • @QuocDatPhung
      @QuocDatPhung  10 หลายเดือนก่อน +1

      Thanks Messi! You can find all of my Calculus II videos in the following link (don't forget to share and kindly subscribe!): th-cam.com/play/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA.html

  • @spaceclottey6250
    @spaceclottey6250 ปีที่แล้ว +2

    super clear, thank you

    • @QuocDatPhung
      @QuocDatPhung  ปีที่แล้ว +1

      You're very welcome! You can find the rest of my Calculus 2 videos here: th-cam.com/play/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA.html

  • @richmondoseitwumasi9975
    @richmondoseitwumasi9975 ปีที่แล้ว +2

    Thank you very much 😊

    • @QuocDatPhung
      @QuocDatPhung  ปีที่แล้ว +1

      You're so welcome Richmond! If you really like my Calculus 2 videos, you can find the rest of them in one place here: th-cam.com/play/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA.html

  • @stanleywainaina1413
    @stanleywainaina1413 ปีที่แล้ว +2

    Thank you mate

    • @QuocDatPhung
      @QuocDatPhung  ปีที่แล้ว +1

      You're very welcome Stanley! Here's the rest of my Calculus 2 videos in this playlist: th-cam.com/play/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA.html

  • @ibrahimtunahandag6081
    @ibrahimtunahandag6081 ปีที่แล้ว +2

    Bro bor bro bro bro bro!!! why we did not choose 1/x instead of 1/x^2?

    • @ibrahimtunahandag6081
      @ibrahimtunahandag6081 ปีที่แล้ว +1

      Is it because of main func. is odd?

    • @QuocDatPhung
      @QuocDatPhung  ปีที่แล้ว +1

      @@ibrahimtunahandag6081 Please let me know the timestamp of this problem, so I can help you with the specific example.

    • @Earlx3n_shorts
      @Earlx3n_shorts 8 หลายเดือนก่อน

      Just trial and error,, both 1/x^2 and 1/x are acceptable 👌

  • @kudakwashemcmillengomba603
    @kudakwashemcmillengomba603 ปีที่แล้ว +8

    Watching this video a few minutes before my test😮....Will come and give some feedback after😂

    • @QuocDatPhung
      @QuocDatPhung  ปีที่แล้ว +4

      Great! How was the test? You can find all of my Calculus II videos here: th-cam.com/play/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA.html

    • @kudakwashemcmillengomba603
      @kudakwashemcmillengomba603 ปีที่แล้ว +6

      This video was so helpful 😭...I just followed the steps nd I sailed through. Definitely subscribing here!!

  • @rajpandya737
    @rajpandya737 2 ปีที่แล้ว +2

    finally makes sense

    • @QuocDatPhung
      @QuocDatPhung  2 ปีที่แล้ว +2

      Thanks Raj! Please subscribe and share; it means a lot!

  • @virendralakhawat1087
    @virendralakhawat1087 8 หลายเดือนก่อน +3

    ❤❤❤❤❤

    • @QuocDatPhung
      @QuocDatPhung  8 หลายเดือนก่อน +1

      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: th-cam.com/play/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA.html

  • @simonsays_0826
    @simonsays_0826 6 หลายเดือนก่อน +2

    I love you

    • @QuocDatPhung
      @QuocDatPhung  6 หลายเดือนก่อน +1

      Thank you! Please don't forget to share with your classmates and kindly subscribe ~ you can find all of my Calculus II videos in this link: th-cam.com/play/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA.html

  • @reemsayed9671
    @reemsayed9671 2 ปีที่แล้ว +3

    Could you please include a translation into Arabic?!

    • @QuocDatPhung
      @QuocDatPhung  2 ปีที่แล้ว +3

      Hi Farida! Thanks for letting me know! I will do some research on how to include other translations :)

    • @reemsayed9671
      @reemsayed9671 2 ปีที่แล้ว +1

      @@QuocDatPhung thanks for paying attention waiting for all your awesome coming vedios with translation into arabic🥰

    • @QuocDatPhung
      @QuocDatPhung  2 ปีที่แล้ว +1

      @@reemsayed9671 Thank you! Please don't forget to subscribe and share with classmates :)) It means a lot!

  • @andikusnadi1979
    @andikusnadi1979 ปีที่แล้ว +2

    cool

  • @NCont-i7g
    @NCont-i7g 10 หลายเดือนก่อน +2

    Truly appreciate those extra problems!

    • @QuocDatPhung
      @QuocDatPhung  10 หลายเดือนก่อน +1

      You're very welcome! You can find all of my Calculus II videos here: th-cam.com/play/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA.html