Fundamental Theorem of Calculus Part 1
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Fundamental Theorem of Calculus Part 1 - Derivatives of Integrals.
In this video I show the FTC part 1 and show 4 examples involving derivatives of integrals.
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Patrick I hope you realize you single handedly get America to pass the AP calculus exam
@patrickjmt
8 жыл бұрын
Ha, not sure about that ;) but I hope I able to help a few people out at least
@fatma2027
8 жыл бұрын
+Jonathan “Jonnay” Naughton not just America :P
@busrayavuz8710
8 жыл бұрын
+patrickJMT also you have followers in Turkiye , thank you so much
@sonek53
8 жыл бұрын
+Jonathan “Jonnay” Naughton also in Jamaica, thanks a mil Patrick
@mohammedherz4199
8 жыл бұрын
why did you use chain rule in the third example . ?
13 years later and these videos are still impactful. Thank you
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
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
6 жыл бұрын
this is my biggest problem with all these textbooks. why is everything so extrapolated?? why can't they condense these concepts?
@JamesOfKS
6 жыл бұрын
Because it's written by Math PHD people.
@maengo2000
6 жыл бұрын
I relate so muchhh Nothing in the textbook makes sense
@kathy9124
5 жыл бұрын
I completely agree! The textbook made me question what I was doing while working through the problem.
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.
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.
@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 : )
This guy is like the bob ross of math. Good shit dude
@Handobolo
10 жыл бұрын
While youre at it search em up on youtube u idiot. Think!
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!
Wow man. Your videos are lifesaving!!!!! If i ever bump into patrick jmt in real life, im buying you a beer.
@patrickjmt
8 жыл бұрын
+MrSVTc0bra i live in austin. come buy me a beer
@hollandgraves1912
8 жыл бұрын
Ohhhh....I'm totally finding you and buying you a beer. Lafayette, Louisiana here.
If teachers/professors explained these topics like you, the world would be full of mathematicians. Thank you for making Calculus simple.
This is literally saving my life right now. So simple it's hard. Exactly.
yes, so long as the lower limit of integration is a constant, it does not get 'used' anywhere
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.
Even ten years after posting this, your explanation and examples still make the most sense.
Learned this yesterday, but I was a bit lost. U explained it perfectly in a few minutes. Bless you.
YOU SIR ARE A FUCKING GENIUS!!!
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!
Damn 15 years later and still the most succinct example on YT
glad you like my videos; i have a ton of stuff of calc 2 and 3 some come back often and tell your friends!
Wish my Calc professor was as good as you. You taught me in 10min what he couldn't in an hour
Very good video! Super clear, shows all the important examples, in less than 10 minutes! Well done!
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.
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!!!!
Thanks Patrick, your 9 minute video helped me out more than my professor's hour long lecture. You da mannnn.
excellent videos, fast, well explained and very detailed... Good Job !!! thanks for the video
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! ♥
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!
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!
Why do I feel like the fundamental theorem of calculus is really just a play on notation?
@sbk1398
8 жыл бұрын
+Marc Rover It is. My Calc teacher said it was the same as integration, but notation was different.
I've watched hundreds of math videos on KZread. I always end up coming back to your videos. I think they are the best made. Thanks for contributing to the math community!
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.
This was excellent sir! Thank you.
bless your soul, this is exactly what i needed clarification on! have a final tomorrow - wish me luck !
@z1lla4
4 жыл бұрын
How'd it go?
I have been watching your videos since middle school and I am a college student now. You're always so reliable!!
thanks for watching for so long :) glad i could help out a bit
last part of first semester calc is usually when one sees this stuff, so i figured now would be a good time for it! : )
SO helpful, thank you. You are a lifesaver.
Wow very clear explanations. Defenitely the best math tutor on KZread.
after one video, i am enlightened. THANK YOU SO MUCH. never stop posting videos.
Saved my academic life!
A simple example based explanation. Thanks.
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 ,,,,
This is one of the best , simple , and clear explanation for the fundamental theorem of calculus . Thanks for your effort.
thanks for teaching me more in 9 minutes than my college professor could do in 3 weeks
you're a God send man, thank you!
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.
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!
Exam in 6 hours, thank you so much.
This is so helpful! I wish you were my teacher (even though you basically are through your videos 😂)
@aadarshprajapati9696
3 жыл бұрын
Your comment is still alive
WOOW MAN!!! YOUR KING. your 3mins worth of explaination was my teacher's week worth.
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.
I LOVE YOU PATRICK
You are the real St. Patrick....
The first minute of this video cleared up over days' worth of confusion. Concise explanations, thanks!
Thanks very much for posting these videos. You literally saved my life.
thx dude ! I'm watching this form Saudi Arabia
1:10 ''it's almost so simple it's hard''
Thank you so much! You explained way better than my professor did. I'm so thankful that you are making tons of videos on KZread! Thank you thank you!
mad man love to you, dude. This just made things so much easier to understand versus merely looking at the theorems alone...
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.
Anyone else just loves the way he says "one"? No just me? ok bye.
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!
Absolute life saver been trying to figure this stuff out for past 3 days.
so the derivative of an integral is just the integrand? thanks!
Just brilliant! Do I even need to attend Engineering lectures anymore? Thanks for the tutorial.
Thank you so much! Your 9 minutes and 25 seconds made more sense to me than an hour of self-tutoring!
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.....
at 7:20, how do you know that 0 is between x^2 and tan(x)?
@damnzhaxual
8 жыл бұрын
+idknuttin And how you know that 1 + 0 + 0 + 2 = 3? Are you kidding me?
@bisharpblade6155
7 жыл бұрын
he said that choosing a value between x^2 and tanx don't matter. Since both are variables, they can be anywhere on the number line.
@JoseMorales-md7cc
7 жыл бұрын
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
7 жыл бұрын
the range of tan(x) is all reals though
@kristanisly7724
6 жыл бұрын
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.
my exam is in 4.5 hours.... cramming much?
@dThapa966
6 жыл бұрын
MrCtown8 yes!!!
@greatcanadianmoose3965
4 жыл бұрын
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
4 жыл бұрын
@@greatcanadianmoose3965 So? How did u do
@greatcanadianmoose3965
4 жыл бұрын
@@johnfei434 No clue. I hope at least an 80
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
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
8 жыл бұрын
my case +1
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!!!
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
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 =)
midterm tomorrow...after this video i don't think ive ever been this happy in my entire life . FINALLY i understand it !!! THANK YOU
This was very informative and had great examples that dealt with all possible scenarios. It is very rare to see such an informative and helpful video. Keep up the good work Patrick!
glad to help. i am not sure what you mean by your last statement: My only question is do you use this instead of "u" substitution because this is on an integral whereas u substitution assumes it is not? could you try to clarify or restate it for dense ole me?!
Patrick... You are by far the best teacher I've had.
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!
I learned more in 10 minutes on KZread than 3 lectures in a row on this, thank you so much.
Dear Uncle Pat, thank you for single handedly giving me the knowledge to pass my calculus class. I hope the family is well.
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.
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.
you are the best just the best.better than my all teachers and professors.you are teaching so simple and it makes very sense on us.after now i wont go to the school i will follow you and all your videos..thank you patrick
Thank you very much, It was really helpful. Explained simply and clearly. Keep up the good work!
you are really AMAZING!!!! im so thankful for these videos! i have a calc exam in 2 hours and this is really saving me right now! god bless you
I cant believe you guys take the trouble to upload these, but they help so much! Thanks
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!!!
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
your videos have helped me understand a whole semesters material in one day........thank you so much
Wow what a simple amazing way to put it I've been struggling so bad with this topic now it's clear as day
Thank you so much man, first time viewing your videos but I'll be sure to spread your tutorials around and such. Very helpful!
Thankyou! Only video I could find that covered all the variations and didn’t over complicate it
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!!
Some professors really can learn from a guy like you. Thank you!
Holy shit why does my teacher/textbook have to make this so complicated. You are a life saver Patrick!
u save my calculus man. i have been struggling with this concept lie the whole quarter... u just solve my problem
I'm actually so happy that a tear ran down my face.. Who said people don't cry out of pure joy!
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!!!!