❖ Fundamental Theorem of Calculus Part 1 ❖

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  • Опубліковано 14 січ 2025

КОМЕНТАРІ • 991

  • @harismyname
    @harismyname 8 років тому +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

  • @jn1384
    @jn1384 9 років тому +806

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

    • @patrickjmt
      @patrickjmt  9 років тому +87

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

    • @fatma2027
      @fatma2027 9 років тому +32

      +Jonathan “Jonnay” Naughton not just America :P

    • @busrayavuz8710
      @busrayavuz8710 9 років тому +6

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

    • @sonek53
      @sonek53 8 років тому +6

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

    • @mohammedherz4199
      @mohammedherz4199 8 років тому +1

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

  • @ryannajames7687
    @ryannajames7687 2 роки тому +14

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

  • @iDarkTea
    @iDarkTea 11 років тому +225

    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 років тому +14

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

    • @JamesOfKS
      @JamesOfKS 7 років тому +7

      Because it's written by Math PHD people.

    • @maengo2000
      @maengo2000 6 років тому +4

      I relate so muchhh Nothing in the textbook makes sense

    • @kathy9124
      @kathy9124 6 років тому +1

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

  • @patrickjmt
    @patrickjmt  15 років тому +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 11 років тому +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 років тому +31

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

    • @Handobolo
      @Handobolo 11 років тому +2

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

  • @mattlopez487
    @mattlopez487 Рік тому +2

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

  • @patrickjmt
    @patrickjmt  15 років тому +3

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

  • @pandabear732
    @pandabear732 6 років тому

    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.

  • @dalebennett3582
    @dalebennett3582 11 років тому +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!

  • @MsCudlub
    @MsCudlub 6 років тому

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

  • @timberwrightsvs480
    @timberwrightsvs480 10 років тому +8

    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!

  • @BSach3211
    @BSach3211 9 років тому +2

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

  • @coolkid6855
    @coolkid6855 9 років тому +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.

  • @MrSVTc0bra
    @MrSVTc0bra 8 років тому +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 років тому +71

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

    • @hollandgraves1912
      @hollandgraves1912 8 років тому +3

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

  • @lindsaygarner9863
    @lindsaygarner9863 11 років тому +10

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

  • @patrickjmt
    @patrickjmt  12 років тому

    glad you like my videos; i have a ton of stuff of calc 2 and 3 some come back often and tell your friends!

  • @Mr.Kitten96
    @Mr.Kitten96 9 років тому +32

    YOU SIR ARE A FUCKING GENIUS!!!

  • @2021Hondacivic
    @2021Hondacivic 6 років тому

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

  • @patrickjmt
    @patrickjmt  16 років тому +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! : )

  • @countesscarmilla1479
    @countesscarmilla1479 Рік тому +1

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

  • @huichuanyang8105
    @huichuanyang8105 8 років тому +6

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

  • @visuaviewer
    @visuaviewer 11 років тому

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

  • @sbk1398
    @sbk1398 9 років тому +4

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

  • @patrickjmt
    @patrickjmt  13 років тому

    @th30n1y0n3 no problem, happy to help!

  • @RogerKlauser
    @RogerKlauser 10 років тому +5

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

  • @MsDeez14
    @MsDeez14 13 років тому

    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.

  • @fadsmfawopefaw
    @fadsmfawopefaw 11 років тому +17

    Saved my academic life!

  • @renakeys7224
    @renakeys7224 13 років тому

    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.....

  • @klam2110
    @klam2110 10 років тому +16

    This was excellent sir! Thank you.

  • @patrickjmt
    @patrickjmt  14 років тому

    @ILOVEGIRLS808 tons: this just says to calculate a definite integral, you integrate, plug in the limits of integration.

  • @SpyrotheDragon97
    @SpyrotheDragon97 9 років тому +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!

  • @jblue3069
    @jblue3069 6 років тому +1

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

  • @BWithEmMarie
    @BWithEmMarie 9 років тому +54

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

  • @patrickjmt
    @patrickjmt  16 років тому

    no problem!

  • @mycommentpwnz
    @mycommentpwnz 10 років тому +47

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

    • @sbk1398
      @sbk1398 9 років тому +4

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

  • @Kevdo92
    @Kevdo92 13 років тому

    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.

  • @rayyan1830
    @rayyan1830 11 років тому +7

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

  • @patrickjmt
    @patrickjmt  12 років тому

    thanks for watching for so long :) glad i could help out a bit

  • @bripeticca8010
    @bripeticca8010 9 років тому +14

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

    • @z1lla4
      @z1lla4 5 років тому

      How'd it go?

  • @drewfield3686
    @drewfield3686 6 років тому

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

  • @8Lightningbolt8
    @8Lightningbolt8 8 років тому +5

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

  • @elementoxygen
    @elementoxygen 15 років тому

    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

  • @kylek395
    @kylek395 7 років тому +3

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

  • @theworldclown
    @theworldclown 12 років тому

    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!

  • @sophc193
    @sophc193 9 років тому +6

    SO helpful, thank you. You are a lifesaver.

  • @mcrockafelladragon
    @mcrockafelladragon 12 років тому

    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!

  • @nathansturgess6809
    @nathansturgess6809 9 років тому +3

    A simple example based explanation. Thanks.

  • @stan719
    @stan719 16 років тому

    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.

  • @khchild
    @khchild 8 років тому +10

    I LOVE YOU PATRICK

  • @segoviapatricio
    @segoviapatricio 10 років тому +8

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

  • @jorgehn7
    @jorgehn7 10 років тому +3

    You are the real St. Patrick....

  • @myooyoke
    @myooyoke 15 років тому

    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
    =)

  • @iLoveTurtlesHaha
    @iLoveTurtlesHaha 7 років тому +9

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

  • @BryceSH1992
    @BryceSH1992 12 років тому

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

  • @zeLcapitaL
    @zeLcapitaL 10 років тому +5

    you're a God send man, thank you!

  • @patrickjmt
    @patrickjmt  16 років тому +2

    thanks for the kind words : )

  • @idknuttin
    @idknuttin 9 років тому +12

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

    • @damnzhaxual
      @damnzhaxual 8 років тому +1

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

    • @JoseMorales-md7cc
      @JoseMorales-md7cc 7 років тому +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 років тому

      the range of tan(x) is all reals though

    • @kristanisly7724
      @kristanisly7724 7 років тому +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.

  • @gideonnovero8228
    @gideonnovero8228 9 років тому +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!!!!

  • @meedoo707sulmi
    @meedoo707sulmi 9 років тому +4

    thx dude !
    I'm watching this form Saudi Arabia

  • @ellurfellur18
    @ellurfellur18 12 років тому

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

  • @sihlemkosi
    @sihlemkosi 7 років тому +3

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

  • @patrickjmt
    @patrickjmt  13 років тому

    @rr5001 it is posted as a video response

  • @ImTooAbstract
    @ImTooAbstract 11 років тому +3

    Exam in 6 hours, thank you so much.

  • @patrickjmt
    @patrickjmt  13 років тому

    @Shallowz987 i do not do online tutoring. i used to tutor in person but i am pretty much done with that too

  • @lesher27
    @lesher27 10 років тому +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.

  • @kinoshitalite
    @kinoshitalite 6 років тому

    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

  • @MrCtown8
    @MrCtown8 11 років тому +48

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

    • @dThapa966
      @dThapa966 7 років тому +3

      MrCtown8 yes!!!

    • @greatcanadianmoose3965
      @greatcanadianmoose3965 5 років тому

      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 5 років тому +1

      @@greatcanadianmoose3965 So? How did u do

    • @greatcanadianmoose3965
      @greatcanadianmoose3965 5 років тому

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

  • @brainsofitall8
    @brainsofitall8 15 років тому

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

  • @kingkrazy0wns
    @kingkrazy0wns 11 років тому +3

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

  • @patrickjmt
    @patrickjmt  14 років тому +1

    @jimmyti9cer the FTC II says that you can evaluate a definite integral by integrating the function and plugging in the limits of integration. i have tons of vids on integration, so take your pick : )

  • @TyTimeIsAwesome
    @TyTimeIsAwesome 13 років тому

    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.

  • @patrickjmt
    @patrickjmt  16 років тому

    god bless the internets.... the best invention of my lifetime

  • @Thorsguard
    @Thorsguard 15 років тому

    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.

  • @raflaagergs2096
    @raflaagergs2096 11 років тому

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

  • @ch3rryp3psi
    @ch3rryp3psi 13 років тому

    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! ♥

  • @krystalfox007
    @krystalfox007 13 років тому

    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!

  • @henryjunior38
    @henryjunior38 12 років тому

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

  • @11KAB11
    @11KAB11 10 років тому +1

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

  • @CricStarSikh
    @CricStarSikh 12 років тому

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

  • @QABBAN
    @QABBAN 12 років тому

    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 ,,,,

  • @LapinAngelique00
    @LapinAngelique00 12 років тому

    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!

  • @patrickjmt
    @patrickjmt  16 років тому

    thanks!

  • @Osiyor
    @Osiyor 15 років тому

    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!!!!

  • @Superpolo1
    @Superpolo1 12 років тому

    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

  • @ginayang95
    @ginayang95 13 років тому

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

  • @bigbadbob357
    @bigbadbob357 15 років тому

    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!!!

  • @djmaverickoop
    @djmaverickoop 16 років тому

    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!!

  • @patrickjmt
    @patrickjmt  13 років тому

    @iitzxniicole learning to read a math text book is hard - it was an acquired skill for me.

  • @joe0404
    @joe0404 8 років тому

    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!

  • @1955stefanie
    @1955stefanie 12 років тому

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

  • @angieangel135
    @angieangel135 14 років тому

    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.

  • @marcush5533
    @marcush5533 6 років тому

    Bro Patrick shout out from the University of Chicago. You're killing it.

  • @rebeckahzdor7361
    @rebeckahzdor7361 12 років тому

    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

  • @KennArc
    @KennArc 13 років тому

    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.

  • @jugglingjon1
    @jugglingjon1 14 років тому

    Thanks for all of the videos! You're not afraid to show us tough problems, it's a great confidence boost to all of us. I'll keep watching!

  • @Killer390
    @Killer390 12 років тому

    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 років тому

    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!!!

  • @BlackStringedWolf
    @BlackStringedWolf 13 років тому

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