Can the trapezoidal rule be better than the midpoint rule for approximating an integral?

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  • เผยแพร่เมื่อ 2 ก.พ. 2025

ความคิดเห็น • 159

  • @rehmmyteon5016
    @rehmmyteon5016 4 ปีที่แล้ว +69

    bprp fans: where is blackpenredpen?
    bprp: i'm back yooo

  • @blackpenredpen
    @blackpenredpen  4 ปีที่แล้ว +50

    Many schools have announced that they will go online in the coming up semester. Hope everyone the best and stay safe from the coronavirus.
    Let me know how the situation in your city.
    Best wish to everyone.

    • @Sg190th
      @Sg190th 4 ปีที่แล้ว +2

      I always knew going online would be useful.

    • @haval00
      @haval00 4 ปีที่แล้ว

      Hey man thanks to God you are back!!! I thought corona virus got you !

    • @subhadeepsarkar5606
      @subhadeepsarkar5606 4 ปีที่แล้ว

      less than 1% of our state has been infected.though we hang near china😂

    • @robsbackyardastrophotograp8885
      @robsbackyardastrophotograp8885 4 ปีที่แล้ว

      Thank you, Steve!

    • @djvalentedochp
      @djvalentedochp 4 ปีที่แล้ว +2

      Heyy you are back again man, here in brazil there are some infected people but it is all under control. I wish you stay safe from the corona virus

  • @akshatahuja2523
    @akshatahuja2523 4 ปีที่แล้ว +103

    After a long time
    Finally
    He is back

    • @blackpenredpen
      @blackpenredpen  4 ปีที่แล้ว +17

      Akshat Ahuja
      I never left! : )

  • @KevinCarretoMendoza
    @KevinCarretoMendoza 4 ปีที่แล้ว +13

    I couldn't follow you on instagram bc it was private:(, but you don't know how happy i am now that you're back!

    • @blackpenredpen
      @blackpenredpen  4 ปีที่แล้ว +6

      Aww thank you!!! My “wear_math” account is public and I will post more there too.

  • @earl8295
    @earl8295 4 ปีที่แล้ว +2

    I've been watching your videos for learning, really learnt a lot from you. I really appreciate what you did for us and your efforts. You earned my respect.

  • @drpeyam
    @drpeyam 4 ปีที่แล้ว +3

    YOU’RE BACK!!!!!! 😍😍😍😍😍😍😍😍😍😍😍😍😍😍

  • @stevemonkey6666
    @stevemonkey6666 4 ปีที่แล้ว +2

    Glad to see you're back

  • @thedoublehelix5661
    @thedoublehelix5661 4 ปีที่แล้ว +2

    You're back!!!!!!!

  • @OonHan
    @OonHan 4 ปีที่แล้ว +5

    YOURE BACK!!!!!

    • @blackpenredpen
      @blackpenredpen  4 ปีที่แล้ว +3

      I never left!! : )
      I did my marathon this past Sunday so yea!

    • @OonHan
      @OonHan 4 ปีที่แล้ว +2

      blackpenredpen Phew!!

    • @blackpenredpen
      @blackpenredpen  4 ปีที่แล้ว +2

      Oon Han yea. I actually have been doing videos all these time too but just not for the main channel. This video was recorded a few days ago too.

    • @OonHan
      @OonHan 4 ปีที่แล้ว

      blackpenredpen that’s reassuring that you are still passionate for Maths!

    • @blackpenredpen
      @blackpenredpen  4 ปีที่แล้ว +2

      I am and will always be.
      It was just nice for me to take a break from uploading on my main channel. In fact, I uploaded this because it was a problem that I had been trying solve for a long time since I started teaching calc 2.

  • @chirayu_jain
    @chirayu_jain 4 ปีที่แล้ว +8

    You're back, yay!

  • @phlogchamp
    @phlogchamp 4 ปีที่แล้ว

    I’m so glad you’re “back,” I missed your videos! Made me think in a different way.

  • @6099x
    @6099x 4 ปีที่แล้ว

    so good to see maths in my subscription feed once again! im so glad you're back

  • @younesabid5481
    @younesabid5481 4 ปีที่แล้ว +3

    Welcome Back 🔥🔥💖

  • @joso5681
    @joso5681 4 ปีที่แล้ว +1

    I'm glad you're back

  • @CDChester
    @CDChester 4 ปีที่แล้ว +4

    As I mentioned earlier functions close to sinusoidal ones T is preferred to M.

  • @Happy_Abe
    @Happy_Abe 4 ปีที่แล้ว +1

    Been awaiting the great return!

  • @dzakytamir3048
    @dzakytamir3048 4 ปีที่แล้ว +1

    Please, don't ever break again. We miss you

  • @gregoriousmaths266
    @gregoriousmaths266 4 ปีที่แล้ว +2

    Hiiii
    The king is back

  • @178fahimahmed7
    @178fahimahmed7 4 ปีที่แล้ว +3

    Good to see you back after a long time ♥️♥️♥️

  • @egillandersson1780
    @egillandersson1780 4 ปีที่แล้ว

    Happy to see you again !

  • @emperorpingusmathchannel5365
    @emperorpingusmathchannel5365 4 ปีที่แล้ว +3

    The king is back!!! Woooh!

  • @jagatiello6900
    @jagatiello6900 4 ปีที่แล้ว

    Glad you're back Steve!

  • @jzanimates2352
    @jzanimates2352 4 ปีที่แล้ว +1

    The legend is back!!!

  • @ProfOmarMath
    @ProfOmarMath 4 ปีที่แล้ว +1

    Nice intuitive build up of the construction.

  • @ismaelescobar8851
    @ismaelescobar8851 4 ปีที่แล้ว

    You're the best at what you do, we miss you

  • @erik-ic3tp
    @erik-ic3tp 4 ปีที่แล้ว

    I'm glad you're back. :)

  • @nilaymarathe2271
    @nilaymarathe2271 4 ปีที่แล้ว +2

    He's back!😲😲

  • @wahyuadi35
    @wahyuadi35 4 ปีที่แล้ว +1

    Finally, BlackPenRedPen welcome back to make another video.. YAY #Hooray #YAY

  • @krukowstudios3686
    @krukowstudios3686 4 ปีที่แล้ว +17

    HE’S BAAAACK!!!! :D :D

    • @blackpenredpen
      @blackpenredpen  4 ปีที่แล้ว +3

      Krukow Studios I never left! : )

  • @Supremer_2
    @Supremer_2 4 ปีที่แล้ว +15

    Oh hi 👋 we missed you

    • @blackpenredpen
      @blackpenredpen  4 ปีที่แล้ว +5

      Johny English
      Aww thank you!!

    • @shambosaha9727
      @shambosaha9727 4 ปีที่แล้ว +6

      @@blackpenredpen Yeah we did. We annoyed Dr πm so much by asking where you were!

  • @minhmouse
    @minhmouse 4 ปีที่แล้ว +2

    welcome back!

  • @AthyXrayGD
    @AthyXrayGD 4 ปีที่แล้ว +3

    HE’S BACK

  • @jannesl9128
    @jannesl9128 4 ปีที่แล้ว

    Nice, youre back!

  • @sumitjade6428
    @sumitjade6428 4 ปีที่แล้ว +2

    Bro can you please make video on use of calculus in daily life

  • @armanrasouli2779
    @armanrasouli2779 4 ปีที่แล้ว +1

    welcome back, sir

  • @uhkneerudh
    @uhkneerudh 4 ปีที่แล้ว +3

    HES BACK BOYSSSSSS!!!!!!

  • @clubstepdj
    @clubstepdj 4 ปีที่แล้ว +2

    Hey, welcome back :D

  • @viewer4229
    @viewer4229 4 ปีที่แล้ว +1

    I love you sir from India!!!

  • @MrMassimoT
    @MrMassimoT 4 ปีที่แล้ว +1

    Finally he's back!!

  • @tipoima
    @tipoima 4 ปีที่แล้ว +2

    Was literally just yesterday checking if you were still around lol

  • @peter-hm9iu
    @peter-hm9iu 4 ปีที่แล้ว +2

    You're back

  • @sehjaan2332
    @sehjaan2332 4 ปีที่แล้ว +3

    Finally you are back sir🙂🙂😊

  • @garyhuntress6871
    @garyhuntress6871 4 ปีที่แล้ว

    Great to see a new video!!!!

  • @Melkboer38
    @Melkboer38 4 ปีที่แล้ว

    You're back 😍

  • @gateway5151
    @gateway5151 4 ปีที่แล้ว

    Sir, can you please make a marathon video on cal 3.

  • @urban_villager
    @urban_villager 4 ปีที่แล้ว

    Mathematics NCERT question integration of e^2x
    sinx

  • @subhadeepsarkar5606
    @subhadeepsarkar5606 4 ปีที่แล้ว +4

    just wanted to say, i found your every video so useful( though i'm a high school student😂)

  • @arynbhar
    @arynbhar 4 ปีที่แล้ว +2

    Where you been last 2 months?

  • @adityarupda1795
    @adityarupda1795 4 ปีที่แล้ว

    Thanks for your video bprp

  • @mannyheffley9551
    @mannyheffley9551 4 ปีที่แล้ว +1

    #Yay you uploaded. I was binge watching all your episodes.

  • @rehmmyteon5016
    @rehmmyteon5016 4 ปีที่แล้ว +22

    congrats on your 4:20 marathon!

  • @bk-sl8ee
    @bk-sl8ee 4 ปีที่แล้ว

    Sir plz tell me which video playlist of yours should I follow to learn calculus from the beginning to advanced level.
    I need your help,sir!
    Thank you sir.

  • @victoremanuel8134
    @victoremanuel8134 4 ปีที่แล้ว

    the best notification I received since your last video!

  • @alkankondo89
    @alkankondo89 4 ปีที่แล้ว +1

    I feel like BlackPenRedPen started posting again mainly because it's Spring Break and he's not currently teaching. I don't know if this is true, but if it is, that's quite hilarious: he just HAS TO let his passion-for-sharing-math out in some way! Also, LOL at 2:15 -- it's not that the example wouldn't work; it's just that it's not that fun! 😆
    Good to see you again, BlackPenRedPen!!

    • @blackpenredpen
      @blackpenredpen  4 ปีที่แล้ว +1

      alkankondo89 thank you!! I was actually doing videos for my students but they were just cut and dry homework solutions so I didn’t post them on my main channel. But yea, I finally had something that I think it would be interesting enough for this channel so here I am!

  • @allmight801
    @allmight801 4 ปีที่แล้ว

    how do you come up with those ideas?

  • @BlackFiresong
    @BlackFiresong 4 ปีที่แล้ว

    You're aliiiiive! Yay :D

  • @urban_villager
    @urban_villager 4 ปีที่แล้ว

    Sir plz please please make an video on integration of e^2x sinx

  • @guilhermeneryrocha4056
    @guilhermeneryrocha4056 4 ปีที่แล้ว

    When life was starting be unbearable
    He came back to save us
    TY

  • @ASAD7273
    @ASAD7273 4 ปีที่แล้ว

    My favourite channel.

  • @Quwertyn007
    @Quwertyn007 4 ปีที่แล้ว

    What about the parabolic approximation

  • @szerednik.laszlo
    @szerednik.laszlo 4 ปีที่แล้ว +3

    "Okay, as we all know.." I'm not sure, sir! :D

  • @williamhewlett4184
    @williamhewlett4184 4 ปีที่แล้ว

    He's alive!

  • @andriusjonaitis8509
    @andriusjonaitis8509 4 ปีที่แล้ว

    Finally a new video ☺

  • @vibhupandya6103
    @vibhupandya6103 4 ปีที่แล้ว

    Where were youuuu???? Missed you sooooo much

  • @CordedHeadphones
    @CordedHeadphones 4 ปีที่แล้ว +1

    finally! I missed my boi

  • @CornishMiner
    @CornishMiner 4 ปีที่แล้ว +1

    Black pen Red pen Yay!

  • @harshitbamotra2013
    @harshitbamotra2013 4 ปีที่แล้ว

    After a long long time the superhero is back.

    • @harshitbamotra2013
      @harshitbamotra2013 4 ปีที่แล้ว

      could you confirm something I have sent you in twitter @blackpenredpen

  • @calcuquack1206
    @calcuquack1206 4 ปีที่แล้ว +1

    The boss can handle the pi-th derivative of x.
    The boss can handle the 1/2th integral of x.
    But can he handle... the xth derivative of x?
    Edit: I meant to say f(x) at the end, not x.

    • @angelmendez-rivera351
      @angelmendez-rivera351 4 ปีที่แล้ว

      Calculus What does taking the xth derivative of f(x) even mean, though? This is totally not well-defined.

  • @Vicky-maayon
    @Vicky-maayon 4 ปีที่แล้ว

    Super bro i am waiting for ur more video

  • @fumiyatomozaki3336
    @fumiyatomozaki3336 4 ปีที่แล้ว +1

    I know the rule but didn't know they have such a beautiful name

  • @anikbhowmick1044
    @anikbhowmick1044 4 ปีที่แล้ว

    Finally after a long gap .you are back ....

  • @shohamsen8986
    @shohamsen8986 4 ปีที่แล้ว

    Technically for the trapezoidal rule to beat the mid point rule, you should show that this is the case for all partitions, or atleast subpartitions of your original partition. It could be that T3 is a better approximation than M3 but T100 onwards is worse than M100. Infact since your curve is non differentiable at one point only, i suspect this will be the case.

    • @blackpenredpen
      @blackpenredpen  4 ปีที่แล้ว +1

      Yea. I agree. The main point that I wanted to show is “midpoint rule” is NOT always better. My thought is to find an integral and a n so that Tn is better than Mn. In this case m, T3 is better than M3 and that satisfies my condition. I should add in the title that (at least for this time) or something like that.

    • @shohamsen8986
      @shohamsen8986 4 ปีที่แล้ว

      @@blackpenredpen yeah but unless its true for all 'n', saying trapezoid is better than midpoint is not really a valid statement. Anyway, welcome back. Its been a long wait.

    • @blackpenredpen
      @blackpenredpen  4 ปีที่แล้ว +1

      Thanks!

    • @angelmendez-rivera351
      @angelmendez-rivera351 4 ปีที่แล้ว

      Shoham Sen It does not hold that for all n, the midpoint rule is better than the trapezoid rule either, though. This is exactly the claim that BPRP proved. He was never required to prove anything different because he never claimed anything different.

  • @kapilaagrawal2560
    @kapilaagrawal2560 4 ปีที่แล้ว

    Do a video on series involving binomial coefficients

    • @blackpenredpen
      @blackpenredpen  4 ปีที่แล้ว

      I did the binomial series already. Is that what you are looking for?

    • @kapilaagrawal2560
      @kapilaagrawal2560 4 ปีที่แล้ว

      @@blackpenredpen I mean questions like,.. Find the sum sigma r=0 to r=5 32C 6r

  • @ivankaticos
    @ivankaticos 4 ปีที่แล้ว

    Hes back bois and girls

  • @anujchincholikar4433
    @anujchincholikar4433 4 ปีที่แล้ว

    If we could collab every maths topics known then what topic would contribute maximum in study of maths ????

  • @nisargbhavsar25
    @nisargbhavsar25 4 ปีที่แล้ว

    Long time no see!!!!!!!

  • @TheNachoesuncapo
    @TheNachoesuncapo 4 ปีที่แล้ว

    Life is good again!

  • @sciencifier3232
    @sciencifier3232 4 ปีที่แล้ว +1

    Why after a long time🤔🤔🤔🤔🤔

  • @marccox8977
    @marccox8977 4 ปีที่แล้ว

    It seems people are stuck thinking of Integrals dx, and dy is just as good or better. So the Most accurate Definite Integral is when average DI-dy Lebesgue integration (red) with DI-dx Riemann integration Riemann (blue) here >>
    en.wikipedia.org/wiki/File:RandLintegrals.png
    To develop this intuition see "Intuitive interpretation" section here >> en.wikipedia.org/wiki/Lebesgue_integration
    .. NOW what if I told you ? ... while this is the most accurate method , it is INtractable / does NOT scale well (yet?) for multivariate Calculus of N-dimensions? In fact it scales horribly on the order of BIG-O(N^N) - maybe walk down the hall and ask your local friendly CS guys for another take ; ALSO I know the software to make this tractable for N-dimensions of large N .. just ask me :-)

  • @MrPanzerTanzer
    @MrPanzerTanzer 4 ปีที่แล้ว +2

    #TeamTrapezoid

  • @TrollBTD
    @TrollBTD 4 ปีที่แล้ว

    Where were you?

  • @alkaverma5974
    @alkaverma5974 4 ปีที่แล้ว

    Finally back

    • @alkaverma5974
      @alkaverma5974 4 ปีที่แล้ว

      I waiting for your video

  • @juniormontalvan4062
    @juniormontalvan4062 4 ปีที่แล้ว

    Here you are! :'D

  • @adityarupda1795
    @adityarupda1795 4 ปีที่แล้ว +1

    Hi bprp i want to ask you my integrals problem so how should i ask you my integrals problem please reply 🙂🙂🙂🤘🤘🤘🤘🤘🙂🙂🙂🙂🤘🙂🙂🙂🙂🙂🤘

  • @Sitanshu_Chaudhary
    @Sitanshu_Chaudhary 4 ปีที่แล้ว +1

    Are your family safe from coronavirus

  • @adityarupda1795
    @adityarupda1795 4 ปีที่แล้ว

    I thought you have left this channel 😯😯😯😯😯😯😯😯🙂🙂🙂🙂🙂

  • @tavaftw
    @tavaftw 4 ปีที่แล้ว

    nice that is reason i got it wrong

  • @alwysrite
    @alwysrite 4 ปีที่แล้ว

    where where you all these days? hope no corona !

    • @blackpenredpen
      @blackpenredpen  4 ปีที่แล้ว

      No, don’t worry.

    • @alwysrite
      @alwysrite 4 ปีที่แล้ว

      @@blackpenredpen oh good to hear, now I can click on your video safely : )

  • @dhruv8908
    @dhruv8908 4 ปีที่แล้ว +1

    Whose kobe??

    • @blackpenredpen
      @blackpenredpen  4 ปีที่แล้ว +1

      A basketball legend who unfortunately left us in January.

  • @FaranAiki
    @FaranAiki 4 ปีที่แล้ว

    Why aren't you famous yet?

  • @cosimobaldi03
    @cosimobaldi03 4 ปีที่แล้ว

    That function doesn't represent that graph

    • @blackpenredpen
      @blackpenredpen  4 ปีที่แล้ว

      Hmm I think it does. I just checked again

  • @VibingMath
    @VibingMath 4 ปีที่แล้ว +1

    Yay finally back man and congrat your great result in marathon!
    For those who know chinese, bprp also uploaded some videos during his break. Go subscribe at the link: th-cam.com/channels/rONDbyO94HIrJyfhS6qfjA.htmlvideos

  • @GhostyOcean
    @GhostyOcean 4 ปีที่แล้ว

    Twitter sneak peek!

  • @firstnamelastname8684
    @firstnamelastname8684 4 ปีที่แล้ว

    i mean, obviously its better for straight lines but anyway

  • @wpbn5613
    @wpbn5613 4 ปีที่แล้ว

    wow i am here

  • @user9287p
    @user9287p 4 ปีที่แล้ว

    Math

  • @marco.giardina
    @marco.giardina 4 ปีที่แล้ว

    Simpson's rule wins.

  • @ieqvilamaria619
    @ieqvilamaria619 4 ปีที่แล้ว

    If I do something in both sides of a equation she won't change nothing, so I'll divide both sides by 0 and she will stay the same, Correct, isn't?

  • @ranjitsarkar3126
    @ranjitsarkar3126 4 ปีที่แล้ว +1

    What shit were you doing all this time.....pls don't late this much period between two videos

  • @lapischicken
    @lapischicken 4 ปีที่แล้ว

    ayyyyyy