❖ Fundamental Theorem of Calculus Part 1 ❖

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  • เผยแพร่เมื่อ 31 ต.ค. 2024

ความคิดเห็น • 994

  • @jn1384
    @jn1384 9 ปีที่แล้ว +807

    Patrick I hope you realize you single handedly get America to pass the AP calculus exam

    • @patrickjmt
      @patrickjmt  9 ปีที่แล้ว +87

      Ha, not sure about that ;) but I hope I able to help a few people out at least

    • @fatma2027
      @fatma2027 8 ปีที่แล้ว +32

      +Jonathan “Jonnay” Naughton not just America :P

    • @busrayavuz8710
      @busrayavuz8710 8 ปีที่แล้ว +6

      +patrickJMT also you have followers in Turkiye , thank you so much

    • @sonek53
      @sonek53 8 ปีที่แล้ว +6

      +Jonathan “Jonnay” Naughton also in Jamaica, thanks a mil Patrick

    • @mohammedherz4199
      @mohammedherz4199 8 ปีที่แล้ว +1

      why did you use chain rule in the third example . ?

  • @ryannajames7687
    @ryannajames7687 ปีที่แล้ว +11

    13 years later and these videos are still impactful. Thank you

  • @harismyname
    @harismyname 7 ปีที่แล้ว +92

    Seriously bro . I don't know about the rest of humanity , but I know for sure you are going to heaven after death.
    You have at least helped thousands of students pass calculas across the globe

  • @iDarkTea
    @iDarkTea 11 ปีที่แล้ว +222

    PatrickJMT, my textbook took 10 pages to explain this in a completely verbose & confusing manner & you did it within a few examples. Thanks a bunch like usual (:

    • @ArtificialVik
      @ArtificialVik 7 ปีที่แล้ว +14

      this is my biggest problem with all these textbooks. why is everything so extrapolated?? why can't they condense these concepts?

    • @JamesOfKS
      @JamesOfKS 6 ปีที่แล้ว +7

      Because it's written by Math PHD people.

    • @maengo2000
      @maengo2000 6 ปีที่แล้ว +4

      I relate so muchhh Nothing in the textbook makes sense

    • @kathy9124
      @kathy9124 5 ปีที่แล้ว +1

      I completely agree! The textbook made me question what I was doing while working through the problem.

  • @patrickjmt
    @patrickjmt  15 ปีที่แล้ว +15

    hey man, glad to help you.
    if someone told me in calc 1 i would be a math major, i still would not have believed them.
    this stuff is (obviously) very deep, and very very interesting i think. it is just all so useful in describing the world around us in some meaningful way. it blows my mind.

  • @sball95
    @sball95 10 ปีที่แล้ว +15

    Patrick. I've spent 4 and a half hours trying to learn this concept from my textbook. You taught it to me in 1/24th of that time. Thank you - Keep doing what you're doing man cuz it's helpful for so many peopl.

  • @Handobolo
    @Handobolo 11 ปีที่แล้ว +31

    This guy is like the bob ross of math. Good shit dude

    • @Handobolo
      @Handobolo 11 ปีที่แล้ว +2

      While youre at it search em up on youtube u idiot. Think!

  • @mattlopez487
    @mattlopez487 11 หลายเดือนก่อน +2

    Damn 15 years later and still the most succinct example on YT

  • @timberwrightsvs480
    @timberwrightsvs480 9 ปีที่แล้ว +7

    This is the way a calculus lesson should be done. Calmly and clearly show the work and don't be afraid to show the (minor) mistakes in notation. There's something about an edited/polished math lesson that taxes my interest. Much like English, mathematics is a language that's taught by learning the letter 'A' first (its simplest component) -- and Patrick does a great job of showing that we're all fallible, yet capable of learning a step at a time. Great job, Patrick!

  • @pandabear732
    @pandabear732 6 ปีที่แล้ว

    My professor took an hour and 15 minutes to explain this concept and never blatantly stated the concept. Thank you SO much, this is so much simpler than it seems.

  • @coolkid6855
    @coolkid6855 9 ปีที่แล้ว +11

    I never comment, Ever, but I just want to say this made this beyond easy to understand and helped me out a lot. Thanks man.

  • @MsCudlub
    @MsCudlub 5 ปีที่แล้ว

    Even ten years after posting this, your explanation and examples still make the most sense.

  • @dalebennett3582
    @dalebennett3582 11 ปีที่แล้ว +5

    patrickJMT, I dont think you understand how helpful you have been to me!
    you literally have helped me through AP Calc in highschool and Calc in College. You are AMAZING!! You make everything understandable!

  • @BSach3211
    @BSach3211 8 ปีที่แล้ว +2

    If teachers/professors explained these topics like you, the world would be full of mathematicians. Thank you for making Calculus simple.

  • @lindsaygarner9863
    @lindsaygarner9863 11 ปีที่แล้ว +10

    This is literally saving my life right now. So simple it's hard. Exactly.

  • @huichuanyang8105
    @huichuanyang8105 8 ปีที่แล้ว +6

    Wish my Calc professor was as good as you. You taught me in 10min what he couldn't in an hour

  • @sbk1398
    @sbk1398 9 ปีที่แล้ว +4

    Learned this yesterday, but I was a bit lost. U explained it perfectly in a few minutes. Bless you.

  • @MsDeez14
    @MsDeez14 13 ปีที่แล้ว

    Your videos are such a valuable resource. The instructions are simple and easy to follow and make sense. I know I couldn't have passed pre calc or calc without your help. It's very generous of you to share your time and knowledge without charging exorbitant fees. I'm always spreading the word about your videos. Thanks a lot.

  • @patrickjmt
    @patrickjmt  15 ปีที่แล้ว +3

    yes, so long as the lower limit of integration is a constant, it does not get 'used' anywhere

  • @renakeys7224
    @renakeys7224 12 ปีที่แล้ว

    our professors make our lives bloody complicated for us sometimes but Patrick simplifies it. Thanks a great deal for your help . they are so clear that every brain can grasp and grab it...u truly are a blessing to me and many others.....

  • @RogerKlauser
    @RogerKlauser 10 ปีที่แล้ว +5

    Thanks Patrick, your 9 minute video helped me out more than my professor's hour long lecture. You da mannnn.

  • @mcrockafelladragon
    @mcrockafelladragon 11 ปีที่แล้ว

    midterm is in 1 week, 1 hour, and 51 minutes. starting my cramming now by going through this playlist. it seems like it is very good for all the basics. thank you!

  • @MrSVTc0bra
    @MrSVTc0bra 8 ปีที่แล้ว +48

    Wow man. Your videos are lifesaving!!!!! If i ever bump into patrick jmt in real life, im buying you a beer.

    • @patrickjmt
      @patrickjmt  8 ปีที่แล้ว +71

      +MrSVTc0bra i live in austin. come buy me a beer

    • @hollandgraves1912
      @hollandgraves1912 8 ปีที่แล้ว +3

      Ohhhh....I'm totally finding you and buying you a beer. Lafayette, Louisiana here.

  • @gideonnovero8228
    @gideonnovero8228 9 ปีที่แล้ว +1

    You my friend have just explain this so easily which I could not understand in my lecture notes. My exam is in 10 hours and this has just click in what I needed to know. Thank you!!!!

  • @BWithEmMarie
    @BWithEmMarie 8 ปีที่แล้ว +54

    This is so helpful! I wish you were my teacher (even though you basically are through your videos 😂)

  • @joe0404
    @joe0404 8 ปีที่แล้ว

    Dude, I'm studying computer science, and all of my questions on youtube lead to your channel. You're extremely intelligent and have helped me so much, between mathematics proofs using induction, to calculus. Thanks a ton man!

  • @Mr.Kitten96
    @Mr.Kitten96 9 ปีที่แล้ว +32

    YOU SIR ARE A FUCKING GENIUS!!!

  • @TyTimeIsAwesome
    @TyTimeIsAwesome 13 ปีที่แล้ว

    7 pages of my calc book reading done in less then 10 minutes...sir I would like to thank you so much. I now understand the concept more then when I was reading the material.

  • @SpyrotheDragon97
    @SpyrotheDragon97 9 ปีที่แล้ว +4

    So my calculus teacher had us watch this video, and then solve the problem of the integral of 2x going to x^3 sint^2 dt.
    Thanks for the extra credit opportunity!

  • @kinoshitalite
    @kinoshitalite 5 ปีที่แล้ว

    im taking an exam today and have been struggling with this topic when i was reviewing but u made me understand it. u r a god

  • @mycommentpwnz
    @mycommentpwnz 9 ปีที่แล้ว +47

    Why do I feel like the fundamental theorem of calculus is really just a play on notation?

    • @sbk1398
      @sbk1398 9 ปีที่แล้ว +4

      +Marc Rover It is. My Calc teacher said it was the same as integration, but notation was different.

  • @Thorsguard
    @Thorsguard 15 ปีที่แล้ว

    Thank you so much. I didn't understand Fundamental Theorem of Calculus till I came across your video. You explain so clearly and the last derivation problem was rather difficult. Classes and textbooks run away from doing those kinds of problems. I appreciate your contributions.

  • @patrickjmt
    @patrickjmt  16 ปีที่แล้ว +4

    last part of first semester calc is usually when one sees this stuff, so i figured now would be a good time for it! : )

  • @myooyoke
    @myooyoke 15 ปีที่แล้ว

    Who needs a prof when i got this!!!!!
    You are the best man... just watching these videos makes me understand like a month of lectures in just 30 minutes
    hats off to you
    =)

  • @nathansturgess6809
    @nathansturgess6809 9 ปีที่แล้ว +3

    A simple example based explanation. Thanks.

  • @Kevdo92
    @Kevdo92 12 ปีที่แล้ว

    I love you. Thank you for teaching me an entire section of our book in 9 minutes and 26 seconds. I wish my professor was capable of doing that without losing me 2 minutes into the lecture.

  • @klam2110
    @klam2110 10 ปีที่แล้ว +16

    This was excellent sir! Thank you.

  • @jblue3069
    @jblue3069 6 ปีที่แล้ว +1

    I like that you show different types of problems!!!!!!!!!

  • @bripeticca8010
    @bripeticca8010 9 ปีที่แล้ว +14

    bless your soul, this is exactly what i needed clarification on! have a final tomorrow - wish me luck !

    • @z1lla4
      @z1lla4 4 ปีที่แล้ว

      How'd it go?

  • @raflaagergs2096
    @raflaagergs2096 11 ปีที่แล้ว

    This is one of the best , simple , and clear explanation for the fundamental theorem of calculus . Thanks for your effort.

  • @fadsmfawopefaw
    @fadsmfawopefaw 11 ปีที่แล้ว +17

    Saved my academic life!

  • @theworldclown
    @theworldclown 11 ปีที่แล้ว

    It's 3 a.m. I'm sitting here, "eating" your vids one by one, hoping that I will pass the Final tomorrow...
    Never truly a fan of math. Sometimes, it felt like I was even scared of it. Those genius teachers out there, they got incredible heads and teaching as if we were just the same.
    It's surprising me how fast I can learn from your vids. You get to the core of complex things swiftly, I love that. I'm glad that there're good men like you in the world, spending time to help others. Thanks a lot!

  • @8Lightningbolt8
    @8Lightningbolt8 7 ปีที่แล้ว +5

    Very good video! Super clear, shows all the important examples, in less than 10 minutes! Well done!

  • @visuaviewer
    @visuaviewer 11 ปีที่แล้ว

    I've watched hundreds of math videos on TH-cam. I always end up coming back to your videos. I think they are the best made. Thanks for contributing to the math community!

  • @kylek395
    @kylek395 7 ปีที่แล้ว +3

    thanks for teaching me more in 9 minutes than my college professor could do in 3 weeks

  • @2021Hondacivic
    @2021Hondacivic 5 ปีที่แล้ว

    A godsend. Better than all the math profs I have combined

  • @lesher27
    @lesher27 10 ปีที่แล้ว +2

    Thank you so much man... My teacher spends 3/4 of class time rehearsing the confusing book language and by the time he does one or two examples I'm so confused by the rhetoric I don't learn a thing.

  • @elementoxygen
    @elementoxygen 15 ปีที่แล้ว

    Hi Patrick
    My son is only grade 4, and can you believe now he is addicted to all your videos.....he is calculus boy now.....now very well up to integration.......he is well grounded now....he is math fun.......you are an Angel.....May God bless you
    Michael

  • @jorgehn7
    @jorgehn7 10 ปีที่แล้ว +3

    You are the real St. Patrick....

  • @stan719
    @stan719 16 ปีที่แล้ว

    I learned more in 9 minutes and 25 seconds then I did in an hour and a half class. Thanks, and I will be returning more often as the AP test nears.

  • @ImTooAbstract
    @ImTooAbstract 11 ปีที่แล้ว +3

    Exam in 6 hours, thank you so much.

  • @ellurfellur18
    @ellurfellur18 12 ปีที่แล้ว

    midterm tomorrow...after this video i don't think ive ever been this happy in my entire life . FINALLY i understand it !!! THANK YOU

  • @sophc193
    @sophc193 9 ปีที่แล้ว +6

    SO helpful, thank you. You are a lifesaver.

  • @ch3rryp3psi
    @ch3rryp3psi 13 ปีที่แล้ว

    you really don't know how much i love you
    like you honestly don't
    i find myself being able to follow along and work 'ahead' of you so to speak (as in before you multiply the derivative, i've already got to that step in my head) - that's when i know i really understand the material. thank you for this video!
    thank you for all your videos! ♥

  • @segoviapatricio
    @segoviapatricio 10 ปีที่แล้ว +8

    excellent videos, fast, well explained and very detailed... Good Job !!! thanks for the video

  • @krystalfox007
    @krystalfox007 13 ปีที่แล้ว

    Dont get me wrong. My Calculus teacher is a fantastic teacher. But I love how you get straight to the point really quickly instead of trying to take time to explain things. I often zone out because my teacher takes to long to do the lesson. You have definitely improved my exam scores. TY!

  • @zeLcapitaL
    @zeLcapitaL 10 ปีที่แล้ว +5

    you're a God send man, thank you!

  • @QABBAN
    @QABBAN 11 ปีที่แล้ว

    I really can't thank you enough for your effort & time . Sometimes I really hate math & anything related to it ( & those times were before watching your videos ) but now , I find it easy . THANK YOU ,,,,

  • @meedoo707sulmi
    @meedoo707sulmi 9 ปีที่แล้ว +4

    thx dude !
    I'm watching this form Saudi Arabia

  • @abdiqanialiyusuf3099
    @abdiqanialiyusuf3099 9 ปีที่แล้ว

    when ever i get confused with calculus chapters I directly go to ur clips and I get understood ......thnks 4 ur never-ending support

    • @pdcx
      @pdcx 8 ปีที่แล้ว

      my case +1

  • @khchild
    @khchild 8 ปีที่แล้ว +10

    I LOVE YOU PATRICK

  • @ginayang95
    @ginayang95 12 ปีที่แล้ว

    The first minute of this video cleared up over days' worth of confusion. Concise explanations, thanks!

  • @sihlemkosi
    @sihlemkosi 7 ปีที่แล้ว +3

    Just brilliant! Do I even need to attend Engineering lectures anymore? Thanks for the tutorial.

  • @Osiyor
    @Osiyor 15 ปีที่แล้ว

    I was trying to read this in my textbook and i got all confused with the way they explained but you my guy made this look easy, now i can complete this damn workshop and homework. You are the best dude! Big Up!!!!

  • @iLoveTurtlesHaha
    @iLoveTurtlesHaha 7 ปีที่แล้ว +9

    Anyone else just loves the way he says "one"? No just me? ok bye.

  • @djmaverickoop
    @djmaverickoop 15 ปีที่แล้ว

    I've been confused as hell in calc and you just summed up 2 class periods in one 9 min video. THANK YOU VERY MUCH!!

  • @rayyan1830
    @rayyan1830 10 ปีที่แล้ว +7

    1:10 ''it's almost so simple it's hard''

  • @countesscarmilla1479
    @countesscarmilla1479 10 หลายเดือนก่อน +1

    I AM GENUINELY ABOUT TO CRY. WOW. THANK YOU.

  • @MrCtown8
    @MrCtown8 11 ปีที่แล้ว +48

    my exam is in 4.5 hours.... cramming much?

    • @dThapa966
      @dThapa966 6 ปีที่แล้ว +3

      MrCtown8 yes!!!

    • @greatcanadianmoose3965
      @greatcanadianmoose3965 4 ปีที่แล้ว

      I did the opposite, I only have 4 courses 2 of which are done, and I have spent the past week redoing every... single.... god... dammed.... assignment.... I spent 7+ hours a day on it for 6 days straight. Finals are tomorrow, if I don't get more than a 90 I will scream.

    • @johnfei434
      @johnfei434 4 ปีที่แล้ว +1

      @@greatcanadianmoose3965 So? How did u do

    • @greatcanadianmoose3965
      @greatcanadianmoose3965 4 ปีที่แล้ว

      @@johnfei434 No clue. I hope at least an 80

  • @11KAB11
    @11KAB11 10 ปีที่แล้ว +1

    Holy shit why does my teacher/textbook have to make this so complicated. You are a life saver Patrick!

  • @idknuttin
    @idknuttin 9 ปีที่แล้ว +12

    at 7:20, how do you know that 0 is between x^2 and tan(x)?

    • @damnzhaxual
      @damnzhaxual 8 ปีที่แล้ว +1

      +idknuttin
      And how you know that 1 + 0 + 0 + 2 = 3?
      Are you kidding me?

    • @JoseMorales-md7cc
      @JoseMorales-md7cc 7 ปีที่แล้ว +1

      I think he might have used the Squeeze Theorem for those limits.
      Basically, he considered all the possible values for both tan(x) and x^2.
      To my understanding, tan(x) is always going to be between -1 and 1. So one could think of tan as this -1 ≤ tan(x) ≤ 1
      Then, the x^2 is real from 0 to infinity. So think of x^2 as this 0 ≤ x^2 ≤ ∞.
      I think he took advantage of 0 in both those functions and used it to separate them into different integrals.
      It might help to think of tan(x) and x^2 as functions instead of as single numbers.

    • @josephlauletta3419
      @josephlauletta3419 7 ปีที่แล้ว

      the range of tan(x) is all reals though

    • @kristanisly7724
      @kristanisly7724 7 ปีที่แล้ว +1

      It doesn't matter what number you use as long as you use the same number in the bottom of the first integral and the top of the second. If he would have used 1 or 2 he would have got the same result.

  • @Cootiecat07945
    @Cootiecat07945 13 ปีที่แล้ว

    Thank the lord for you! I have a calculus final tomorrow and I'm freaking out. You are simply the best....oh my god.

  • @kingkrazy0wns
    @kingkrazy0wns 10 ปีที่แล้ว +3

    so the derivative of an integral is just the integrand? thanks!

  • @jwmcmac
    @jwmcmac 14 ปีที่แล้ว

    You have a great gift to simplify.
    Many professors do the opposite . . . they complicate.
    GOD Bless you and us all.

  • @brainsofitall8
    @brainsofitall8 14 ปีที่แล้ว

    I learned more in 10 minutes on TH-cam than 3 lectures in a row on this, thank you so much.

  • @TheCupcakeCharm
    @TheCupcakeCharm 8 ปีที่แล้ว

    I have been watching your videos since middle school and I am a college student now. You're always so reliable!!

  • @SS1v3k1
    @SS1v3k1 15 ปีที่แล้ว

    A few weeks worth of lecturing in a few minutes, now I can practice more, thanks a lot!

  • @michaeldalton7070
    @michaeldalton7070 7 ปีที่แล้ว

    Dear Uncle Pat, thank you for single handedly giving me the knowledge to pass my calculus class. I hope the family is well.

  • @drewfield3686
    @drewfield3686 5 ปีที่แล้ว

    Thankyou! Only video I could find that covered all the variations and didn’t over complicate it

  • @LapinAngelique00
    @LapinAngelique00 11 ปีที่แล้ว

    Thank you for this video! Between how I learned calc in high school, how my profs taught me in college, and what my teaching assistants taught in recitation, I had started to get confused on how to even approach the problem. Thank you for helping me sort out my calculus skills!

  • @BryceSH1992
    @BryceSH1992 12 ปีที่แล้ว

    WOOW MAN!!! YOUR KING. your 3mins worth of explaination was my teacher's week worth.

  • @bigbadbob357
    @bigbadbob357 15 ปีที่แล้ว

    Thanks buddy! I learned more in your 9min 25 second presentation than I did scratching my head for a 1/2 hour reading the text.. but now the text book makes sense too... keep up the good work my man!!!

  • @gingerlady13
    @gingerlady13 7 ปีที่แล้ว

    dude, i was stuck on my calc homework for over three hours. then if ound your video and i finished it in 20 minutes. thank youuu

  • @amatullahkamal
    @amatullahkamal 6 ปีที่แล้ว

    Thank you so much! Your 9 minutes and 25 seconds made more sense to me than an hour of self-tutoring!

  • @rebeckahzdor7361
    @rebeckahzdor7361 11 ปีที่แล้ว

    Thanks to you, I've maintained a high A in my AP Calc class!! Without these videos, I'd be so lost... but you make it easy, simple, and even fun! Thank you so much for all the time you put into these videos. They're really helping a lot of people further their education!! :D

  • @CricStarSikh
    @CricStarSikh 11 ปีที่แล้ว

    Dude...I LOVE YOU...You are 200 billion times better than any of the professors at my University!

  • @Killer390
    @Killer390 12 ปีที่แล้ว

    mad man love to you, dude. This just made things so much easier to understand versus merely looking at the theorems alone...

  • @alanloo7680
    @alanloo7680 12 ปีที่แล้ว

    Your videos are extremely clear and helpful. Because of you homework is a breeze, I even understand everything so well that I help other people outside of class. Please do not stop making videos; I'm going to need you for Calculus 2 & 3!!!

  • @Superpolo1
    @Superpolo1 12 ปีที่แล้ว

    OMG THANK YOU MAN !!! I was looking over my books and lecture notes and you have accomplished something those 2 couldn't do in 2 hours in just one video. KEEP UP THE GOOD WORK :D

  • @henryjunior38
    @henryjunior38 11 ปีที่แล้ว

    Wow very clear explanations. Defenitely the best math tutor on TH-cam.

  • @angieangel135
    @angieangel135 13 ปีที่แล้ว

    oh god oh god, I've got a midterm tomorrow on 1 variable calculus, and it's been two years since I've done any calculus!! Time to have a PatrickJMT videos marathon.

  • @slashfan10
    @slashfan10 16 ปีที่แล้ว

    these videos are great! my professor can lecture on this for an hour and a half and im totally lost, but then i watch these videos and everything clicks in place, Thanks!

  • @KennArc
    @KennArc 12 ปีที่แล้ว

    Aaaaah I love these videos, I always just bearly miss the gist of how to do these, but your videos are really clear and I can rewind and stop wherever that part is I got lost. Awesome. Thank you.

  • @1955stefanie
    @1955stefanie 12 ปีที่แล้ว

    I'm actually so happy that a tear ran down my face.. Who said people don't cry out of pure joy!

  • @SmashedFish76
    @SmashedFish76 12 ปีที่แล้ว

    AP Calc exams tomorrow, and I still don't know the FTC pt. 1 by name? First thing that came to mind was "check patrickJMT". 9 minutes later, I realize how simple it is. Thanks a bunch.

  • @nichellezinck
    @nichellezinck 11 ปีที่แล้ว +1

    I have a calculus exam in two hours and you literally just saved my ass. THANK YOU.

  • @fibertoys
    @fibertoys 16 ปีที่แล้ว

    its astounding how little views you have, although you are a very good teacher in all your videos, good pace, great understanding, and easy to follow steps.

  • @eviltwin1000
    @eviltwin1000 15 ปีที่แล้ว

    Wow you are sooo much better than my calculus professor! My professor makes the easiest things look difficult and confusing but you make it look so easy! Thanks!

  • @BlackStringedWolf
    @BlackStringedWolf 13 ปีที่แล้ว

    Patrick... You are by far the best teacher I've had.

  • @mushroomme96
    @mushroomme96 11 ปีที่แล้ว

    after one video, i am enlightened. THANK YOU SO MUCH.
    never stop posting videos.