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❖ The Definite Integral - Understanding the Definition ❖

  Рет қаралды 835,814

patrickJMT

patrickJMT

Күн бұрын

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) / patrickjmt !! The Definite Integral - Understanding the Definition. In this video, I discuss the definition only; I do not calculate any definite integrals.

Пікірлер: 406
@TamNguyenMinh-op7iq
@TamNguyenMinh-op7iq 8 ай бұрын
It's 2023 now and your videos have helped me with Calculus in College. Thank you so much.
@AndrewSmithDev
@AndrewSmithDev 7 жыл бұрын
Why am I paying 1000 dollars to attend a class where my professor is completely worthless at explaining these ideas when I can come on youtube and get a better explanation for free
@patrickjmt
@patrickjmt 7 жыл бұрын
you can go to Patreon and be a supporter for $1 / mo :)
@robertwilsoniii2048
@robertwilsoniii2048 7 жыл бұрын
That's just not true. Some schools really are worth the money, and the instructors depth of knowledge really can help you out.
@user-or5xy4ht2l
@user-or5xy4ht2l 6 жыл бұрын
because you are reach and kind?
@serinacat4781
@serinacat4781 4 жыл бұрын
Yes, and I paid more than you
@ericfricke4512
@ericfricke4512 4 жыл бұрын
@@robertwilsoniii2048 They said "my professor."
@birdflocked
@birdflocked 10 жыл бұрын
You are a lifesaver when Calculus starts to get confusing.
@patrickjmt
@patrickjmt 15 жыл бұрын
i am very well aware that you can use left endpoints, right endpoints, midpoints, or... ANY POINT AT ALL. : ) if you zoom in on my pictures, you will see that i do not put the dots at the precise middle of each interval, so i am not using the mid points. i appreciate the fact that you think i have no clue whatsoever about what i am doing though
@erikaluna6187
@erikaluna6187 9 жыл бұрын
Patrick you da man
@patrickjmt
@patrickjmt 9 жыл бұрын
+Erika Luna that's not what my wife says...
@patrickjmt
@patrickjmt 9 жыл бұрын
you said it
@gauchoconponcho
@gauchoconponcho 8 жыл бұрын
+Erika Luna Totally agree.
@aveiolofijazzy2248
@aveiolofijazzy2248 8 жыл бұрын
+Erika Luna im saying fam! man is already a legend
@subhradeepbanerjee554
@subhradeepbanerjee554 7 жыл бұрын
hi erika
@cherriewong5852
@cherriewong5852 10 жыл бұрын
Thank you Patrick! Never did i feel bored when watching your enthusiastic calculus teaching! Because of your clear and detailed explanations, I eventually excelled in my final !!!!YOU ARE AWESOME!!!
@MrMoeqt
@MrMoeqt 11 жыл бұрын
You're amazing! You and Khan academy helped me start my calculus. Right now I'm 13, and I started learning basic derivatives at late 12, at first it was so hard, it just looked like d's and x's etc... But I stuck at it and then I finally understood the power rule for taking derivatives, I FELT LIKE A GENIUS:D. From then on I kept going and eventually my knowledge of derivatives came to the point where I can find any derivatives easily, now I'm moving on to integrals because of you! Thanks loads!
@yunisguliyev3815
@yunisguliyev3815 Жыл бұрын
you are 22 now ))
@QWEEKEN73
@QWEEKEN73 10 жыл бұрын
Cal final in 4 hours. Your a life saver!
@patrickjmt
@patrickjmt 15 жыл бұрын
in fact, i never mention anything at all about taking a point in the middle.... you just conclude that from my crappy picture cause you have your own personal impressions of the problem already : ) forget what you know, and just listen to what i say, and then you will see it is all correct
@patrickjmt
@patrickjmt 15 жыл бұрын
good luck in your class and with your future : ) that would be a cool success story for both of us!! : ) drop a line if you have any questions!! and regardless of getting into the #1 school or not, never give up!!!!
@gaoalexander73
@gaoalexander73 9 жыл бұрын
My professor explained this to me in class today. I must say that I was clueless. Maybe its the fact that he assumes its easy since he already understands it, but not you. You assume that we are clueless, which is a good thing. You just made my day a lot better!
@Salamero500
@Salamero500 13 жыл бұрын
seriously you should be getting some kind of nobel prize for teaching excellence, your public service should be recognized some day by all of your students you never met, thank you kindly.
@Renee11123
@Renee11123 10 жыл бұрын
Thank you so much! I'm at the point of calculus where things began to become a whole other language to me and my mind is still trying to process things even at night ruining my sleep. This video helped clear the fog in my mind.
@scorpion2508
@scorpion2508 8 жыл бұрын
Thank God for youtube!!! Your video filled in all the holes or questions i had from class lecture beautifully....Words can't capture the relief of finally "getting it". Thx
@patrickjmt
@patrickjmt 15 жыл бұрын
that, my friend, is truly the magical part
@amandaoliver8679
@amandaoliver8679 8 жыл бұрын
I love your vids but the sound quality on this one makes it unbearable to watch.
@kevincooper2954
@kevincooper2954 6 жыл бұрын
you are getting free education and still complaining. just go and listen to music instead watching education videos.
@serinacat4781
@serinacat4781 4 жыл бұрын
I agree
@seanki98
@seanki98 4 жыл бұрын
it's from 2008
@MonkoGames
@MonkoGames 3 жыл бұрын
the APPROximation
@suyvairu
@suyvairu 6 жыл бұрын
Wooooowwww this video saved me from insanity!!!! Thanks
@macmos1
@macmos1 11 жыл бұрын
These videos are just awesome to watch after reading my calculus book until you fully understand it. It reinforces what I've learned.
@CamiloSanchez1979
@CamiloSanchez1979 14 жыл бұрын
This is incredible ... my old teacher couldn't get me to understand this concept in 4 years....4 years repeating the same subject that is!
@Zeppelinpuppy
@Zeppelinpuppy 10 жыл бұрын
Amigo, thank you so much.you are my hero. Saludos from Argentina
@ablackknightcalledreality1342
@ablackknightcalledreality1342 8 жыл бұрын
Hey Patrick, Just wanted to thank you for all the videos, really helped a lot through my final months of secondary school and final weeks of exams. Keep up the good work, A satisfied student.
@lololol559
@lololol559 4 жыл бұрын
12 years later, this video still is relevant and helpful. Thank you, patrick :D Have a blessed year ahead!
@patrickjmt
@patrickjmt 4 жыл бұрын
this video will be relevant so long as humans exist :)
@Pro22Bro
@Pro22Bro 10 жыл бұрын
you'r better than any prof i've ever had for math
@IbombYourAss
@IbombYourAss 11 жыл бұрын
I can't tell you how much I appreciate your videos - my Calculus class is in the morning, and when I try to do practice problems after class, I can't remember anything I 'learned.' Not only do your videos help me relearn it, it helps me remember what we actually did in class, so I strengthen my understanding even more.
@patrickjmt
@patrickjmt 15 жыл бұрын
yes, i know what your comment was directed towards : )
@Hulahoopish
@Hulahoopish 4 жыл бұрын
I just got my degree in mechanical engineering, and I want you to know, that legitimately might not have happened without you. I cannot thank you enough for these tutorials.
@magicguy1988
@magicguy1988 10 жыл бұрын
Approximation is the foundation of all of single-variable calculus. When trying to understand tangents, we started with an approximation and arrived at the derivative thru use of limits
@nickschor
@nickschor 14 жыл бұрын
Further confirmation that oftentimes the idea behind the exercise is more important than the exercise itself! Thank you again...I'm swearing off of crappy reality tv shows and am going over my old math texts just to see why we did all this in the first place.
@ArdyCakes
@ArdyCakes 15 жыл бұрын
Thanks. I am a ditz when it comes to math and I've failed calc before. I am finally beginning to understand stuff by watching your videos.
@AlannOi
@AlannOi 7 жыл бұрын
"The way we mathematically say use more rectangles" this makes so much more sense now..thank you!!
@milessabin5097
@milessabin5097 9 жыл бұрын
52 seconds in and I understand this more than 6 hours (3 classes) at school.
@Ammm649
@Ammm649 13 жыл бұрын
u r the best i ever seen teaching math and calc i even didnt attend any class of calculas and i pass thnx alot and as u say spread the world with ur knowledge
@pcbingemaster
@pcbingemaster 8 жыл бұрын
so integration is nothing but a quick general way through which one is able to calculate the area below a f(x) without doing n(chunks of delta x) operations? i think i just died from a brainfart!
@patrickjmt
@patrickjmt 15 жыл бұрын
it represents any point from the 'i-th' interval (it does not have to be a left endpoint or right endpoint, etc)
@DrGeemoney
@DrGeemoney 11 жыл бұрын
You are the only reason i am not failing my calc class.... THANK YOU!!!
@Abel_The_
@Abel_The_ 5 жыл бұрын
really it helps me a lot. i after i see your video and when things become so clear and easy to understand i thought my teacher was keeping secrets from me. thank you so much really.
@FranklyLate
@FranklyLate 14 жыл бұрын
PatrickJMT: Excellent video. Lucid and in 9 minutes! Everytime you share knowledge you grow the world a little more and make it a little safer and better to live in. cheers
@seancassity6594
@seancassity6594 11 жыл бұрын
You're the man Patrick, that's all I have to say. Thank you for being such a stud.
@CReePiNxMeaDoWs
@CReePiNxMeaDoWs 11 жыл бұрын
Explained it crystal clear and I just now understand it the night before my Calc I final. You sir, are a life saver and I applaud your work.
@IDidactI
@IDidactI 12 жыл бұрын
When you differentiate, you divide a tiny slice of y by a tiny slice of x i.e. dy/dx. That ratio gives you a slope, which hopefully you understand. So, dy/dx = f'(x). Okay so what happens if we multiply both sides of that by dx, we get dy = f'(x) * dx. So to find y, add up all the 'dy's. That's what the integral does. Also, look at the equation. f'(x) is the height of the function and dx is the width. Area of a rectangle = height * width, right? You can figure out the rest ;)
@yousafs9837
@yousafs9837 8 жыл бұрын
You the real MVP. really though. thank you :)
@aditichaudhary9529
@aditichaudhary9529 5 жыл бұрын
I did not understand this in 4 hours of my math class but you made it seem simple in just 9 mins! Thank You!!
@samarthsai9530
@samarthsai9530 7 жыл бұрын
Well, take that as a suggestion and/or complement:- Some people make their videos with very good quality, animation, graphics but they do not have an elegant teaching style as yours. You are an absolute genius in teaching but the video and audio quality..haha. If Patrick's videos are supplemented with good quality..... Mathematical heavens are going to come down to the earth. Thanks for your great efforts.
@jakedodsonjake
@jakedodsonjake 11 жыл бұрын
khan academy is my usual go to, when i dont get something, but you are proving to actually help me understand better and faster. You are my new go to hahaha.
@Medgy26
@Medgy26 10 жыл бұрын
Thank you so much! My math teacher isn't even out of grad school yet and I have never taken calculus. These videos are lifesavers
@deepika3ful
@deepika3ful 11 жыл бұрын
I really appreciate your effort in these videos. I am taking Applied Calculus I and II both at the same time this semester. Both of my classes are online but I haven't seen any lecture videos from my professor so far because your videos are teaching me almost everything I need to learn. Thank you very much and yea I have all "A"s . All thanks to you.:)
@CirkusBolgen
@CirkusBolgen 16 жыл бұрын
Thankyou patrickJMT; I will recommend your video(s) to the rest of my class.
@Starfallist
@Starfallist 12 жыл бұрын
@Starfallist Now we will derive the function A(x) from these two equations. First, realize that: lim h->0 A(h) = A(x+h)-A(x) = f(x)h, so lim h->0 A(x+h)-A(x) = f(x)h. Now divide both sides by h: lim h->0 [A(x+h)-A(x)]/h = f(x) Do you remember the expression in the LHS? (Say "yes"!) It is the formula for the derivative of A(x). Hence, f(x) is the derivative of A(x), so A(x) is the antiderivative or indefinite integral of f(x).
@bluchamp
@bluchamp 14 жыл бұрын
Thank you. Much easier to understand when it's taught correctly. I swear teachers make things harder than they need to be.
@CallOFDutyMVP666
@CallOFDutyMVP666 12 жыл бұрын
I find it amazing that you can add up an infinite number of infinitesimal cross sections and get a finite value.
@edwardray6401
@edwardray6401 5 жыл бұрын
You made that easy to understand. Now I'm looking for why. Thanks!
@tikiman99099
@tikiman99099 12 жыл бұрын
You have taught me more in 9 minutes than my teacher did all semester, you are a saint. Keep it up buddy!
@Ruddog12
@Ruddog12 11 жыл бұрын
your a true blessing man your getting me through college
@QuanSai
@QuanSai 15 жыл бұрын
You're the teacher I aim to be! You're the man, dude.
@catagon12345
@catagon12345 13 жыл бұрын
I have a test tomorrow, your vids are really helping me study
@michaelelliotbrownle
@michaelelliotbrownle 8 жыл бұрын
You're a gem, mate. Cheers from Ontario
@puff1puff1pass
@puff1puff1pass 11 жыл бұрын
from Saudi Arabia, thanks a lot for these videos really help me
@Vaulter816
@Vaulter816 11 жыл бұрын
you explained everything way better than my calc teacher did!
@revolutiongames2004
@revolutiongames2004 15 жыл бұрын
yes, as i remember, if your function is f(x), the arc length between x=a and x=b is: integral[b,a]( sqrt( 1 + [f '(x)]^2) dx that should give you one of the sides, do the same thing to the other side and sum them together. you can find where the functions cross by setting them equal to each other, and solving for x
@jashvasanwala8514
@jashvasanwala8514 8 жыл бұрын
A awesome video which helped to score 100 marks in my exam thankksss ssssoooo much
@TRUNKER76
@TRUNKER76 14 жыл бұрын
Wow that was super clear and easy to understand! I am doing this stoned and I only had to watch it once!!! lol you rock man I'm seriously considering donating.
@patrickjmt
@patrickjmt 16 жыл бұрын
ha! thanks! no worries about making a donation : ) my main goal for now is to empower people who are willing to take the time to find some extra resources. hopefully mine is one which will help them, if only a little bit, in their 'mathematical life' : )
@5iftyse7en
@5iftyse7en 16 жыл бұрын
yes please.. i like maths but i cant find the right tutor for me.. but you seem to be doing all the right things to make it easier for me.. and trust me even IF u did pay for subscribing vids. i will pay.. Knowledge is priceless i know that much!
@SteU4IA
@SteU4IA 10 жыл бұрын
A perfect and concise example.
@Johanthegnarler
@Johanthegnarler 16 жыл бұрын
I like to come on youtube and reinforce my knowledge of calculus. So far this strategy has worked! 98% in my college calculus class so far, and I have you to thank in part! It helps me to really understand theorems and see how they are derived. Thank you for the effort you put into these videos! They really help a lot. :)
@trabowerling71
@trabowerling71 6 жыл бұрын
Patrick, I can't thank you enough for posting these videos. You have my donation money. I will be periodically donating throughout my career to give thanks. Please keep up the great work.
@Thermidorian
@Thermidorian 15 жыл бұрын
i'm in my last year at the university ,i study Electronics and i did a lot of math ,but never this truly genius demonstration for The Definite Integral...i like the way you present the lessons here on KZbin Greetings from Romania!
@mrproxj
@mrproxj 7 жыл бұрын
Thanks, I now understand. Though the sound quality was poor, I'm glad I watched until the end
@jetswhiteout961
@jetswhiteout961 9 жыл бұрын
Passed calc 1 with a C thanks to your vids, khan academy, and grants tutoring.
@SvetlanaSuperturbo
@SvetlanaSuperturbo 12 жыл бұрын
Thanks for this. I was struggling with understanding the definisjon. Totally helped me.
@patrickjmt
@patrickjmt 16 жыл бұрын
glad the vids help
@Hugotheman88
@Hugotheman88 9 жыл бұрын
Thanks it helps when someone explains concepts and the thought behind a concept instead of just memorizing steps!
@SanSooKungFu
@SanSooKungFu 15 жыл бұрын
Thanks for posting this, and other videos. Nice job of keeping the camera zoomed on the white board.
@MakeMeBadKornPorn
@MakeMeBadKornPorn 14 жыл бұрын
you make things a lil more simple, thank you very very much
@patrickjmt
@patrickjmt 15 жыл бұрын
well, i explain that it does not matter which point in the interval you use; it is irrelevant, which is why i introduced the 'x sub i star' notation
@Jefff72
@Jefff72 11 жыл бұрын
I did up to Multivariable Calc in 1999 and hardly remember this stuff. I going to try to refresh my memory and hopefully bring some of this back.
@CkyYEN
@CkyYEN 9 жыл бұрын
thank you!! it really helpful for me to understand about this concept!!
@FakeAssHandsomeMcGee_
@FakeAssHandsomeMcGee_ 15 жыл бұрын
true...he gets to the point and does it great
@patrickjmt
@patrickjmt 13 жыл бұрын
@Charounson are you sure you are not taking the derivative of an integral (is that the question?)
@ohmannhey
@ohmannhey 15 жыл бұрын
You say that "You can think of it as being an area when the function is above the x-axis." That does apply to areas below the x-axis only that they will be negative and therefore subtracted from the positive area. If seeking for the total area you would have to find the "Schnittpunkte" (German for the zeropoints? ... sorry don´t know the English term) in order to isolate the different segments. No? Great show ... wish schools worldwide would have you teaching skills ... Helping me a lot!
@tincata90
@tincata90 15 жыл бұрын
this really really helped. thnks man MR. Pat. u saved me ALOT of time
@patrickjmt
@patrickjmt 13 жыл бұрын
@Charounson otherwise, you would have to use a series expansion
@Billy193
@Billy193 6 жыл бұрын
This is precisely what I needed! I've been confused about this for so long?
@j44fff
@j44fff 12 жыл бұрын
i was going crazy not understanding this.....thnx man!
@Nelorina
@Nelorina 8 жыл бұрын
Thank you so much, you explain this SO much better than any other video or textbook!
@Billy193
@Billy193 6 жыл бұрын
This is precisely what I needed!
@erigirl08
@erigirl08 15 жыл бұрын
Best thing I have ever found on youttube!!!!
@snowe8640
@snowe8640 10 жыл бұрын
i like the video..only problem is your microphone squeaks sometimes and my headphones and ears disagree with that strongly
@phoenixforger
@phoenixforger 11 жыл бұрын
Two things: This video helped me so much! And I love the way you write your sigmas.
@evinpolack
@evinpolack 14 жыл бұрын
You truly are the king man
@methman1992
@methman1992 11 жыл бұрын
I am going to recommend you to my entire engineering class! thank you for the great videos!
@patrickjmt
@patrickjmt 15 жыл бұрын
u are most welcome
@123XTSK
@123XTSK 4 жыл бұрын
Out standing presentations....each one of yours.Excellent teacher and clarity in sequence of explanations.
@kkevinparkk
@kkevinparkk 10 жыл бұрын
The sound quality though...
@ashleighniriain
@ashleighniriain 12 жыл бұрын
you are my hero....!! I finally understand, just in time for my exam haha
@NineMillimeterKO
@NineMillimeterKO 14 жыл бұрын
I'm now im 10th grade and my math teacher once told me you could calculate the area under a curve, so a week after that I was laying in bed and thinking about what she said , and then I came up with the idea that would take the average y multiplied by delta x , havent learned about limits tho but this video basicly showed me that my idea was just perfect , I'm really glad that I basicly came up with the idea of calculating it and we didn't learn at school yet :o
@carlosfernandez1989
@carlosfernandez1989 14 жыл бұрын
This video was incredibly helpful. Your videos will help me get through calculus 2 this semester. thank you for taking the time to make this
@amrelseweifi5640
@amrelseweifi5640 9 жыл бұрын
Thanks, man! This video was really helpful!
@therock343
@therock343 13 жыл бұрын
WOOOWW... 2 hr Confusiing Lecture vs. 9 min Clear and simple Video.. Omg.. I love you Man! All Homo! haha
@tokio2t
@tokio2t 14 жыл бұрын
I finally understand what that formula means, thanks a lot! your very clear and I appreciate all the effort you take to make your videos.
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