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 (:
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.
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.
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!
@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 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!
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!
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!!!!
well, it is hard to understand. i am showing mechanical procedures on how to solve the problems - but i am not really discussing the theory of what is 'going on'. the theory is what is hard, pushing symbols around is easy once you learn the patterns!
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!
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!
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.
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.....
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.
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!
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.
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.
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
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.
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.
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 =)
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?!
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
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! ♥
Thats it...oh my god my professor kept giving us fresnal integrals like sin(x^2) and cos(e^x). I thought you need to take the integral and do top minus bottom but no one in the class knew how to integrate the functions LOL. Thanks to your video, I realize you don't even need to take the integral...THANK YOU!
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!
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 ,,,,
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.
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
13 years later and these videos are still impactful. Thank you
Patrick I hope you realize you single handedly get America to pass the AP calculus exam
Ha, not sure about that ;) but I hope I able to help a few people out at least
+Jonathan “Jonnay” Naughton not just America :P
+patrickJMT also you have followers in Turkiye , thank you so much
+Jonathan “Jonnay” Naughton also in Jamaica, thanks a mil Patrick
why did you use chain rule in the third example . ?
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 (:
this is my biggest problem with all these textbooks. why is everything so extrapolated?? why can't they condense these concepts?
Because it's written by Math PHD people.
I relate so muchhh Nothing in the textbook makes sense
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.
Damn 15 years later and still the most succinct example on YT
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.
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 guy is like the bob ross of math. Good shit dude
While youre at it search em up on youtube u idiot. Think!
Even ten years after posting this, your explanation and examples still make the most sense.
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.
If teachers/professors explained these topics like you, the world would be full of mathematicians. Thank you for making Calculus simple.
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!
@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 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!
Wow man. Your videos are lifesaving!!!!! If i ever bump into patrick jmt in real life, im buying you a beer.
+MrSVTc0bra i live in austin. come buy me a beer
Ohhhh....I'm totally finding you and buying you a beer. Lafayette, Louisiana here.
yes, so long as the lower limit of integration is a constant, it does not get 'used' anywhere
A godsend. Better than all the math profs I have combined
This is literally saving my life right now. So simple it's hard. Exactly.
I AM GENUINELY ABOUT TO CRY. WOW. THANK YOU.
Wish my Calc professor was as good as you. You taught me in 10min what he couldn't in an hour
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
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!
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!!!!
Learned this yesterday, but I was a bit lost. U explained it perfectly in a few minutes. Bless you.
well, it is hard to understand.
i am showing mechanical procedures on how to solve the problems - but i am not really discussing the theory of what is 'going on'. the theory is what is hard, pushing symbols around is easy once you learn the patterns!
Thanks Patrick, your 9 minute video helped me out more than my professor's hour long lecture. You da mannnn.
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!
Saved my academic life!
Thankyou! Only video I could find that covered all the variations and didn’t over complicate it
This is so helpful! I wish you were my teacher (even though you basically are through your videos 😂)
Your comment is still alive
@ILOVEGIRLS808 tons: this just says to calculate a definite integral, you integrate, plug in the limits of integration.
thanks for teaching me more in 9 minutes than my college professor could do in 3 weeks
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!
YOU SIR ARE A FUCKING GENIUS!!!
glad you like my videos; i have a ton of stuff of calc 2 and 3 some come back often and tell your friends!
last part of first semester calc is usually when one sees this stuff, so i figured now would be a good time for it! : )
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.
Anyone else just loves the way he says "one"? No just me? ok bye.
I like that you show different types of problems!!!!!!!!!
bless your soul, this is exactly what i needed clarification on! have a final tomorrow - wish me luck !
How'd it go?
Holy shit why does my teacher/textbook have to make this so complicated. You are a life saver Patrick!
This was excellent sir! Thank you.
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.....
Why do I feel like the fundamental theorem of calculus is really just a play on notation?
+Marc Rover It is. My Calc teacher said it was the same as integration, but notation was different.
I have been watching your videos since middle school and I am a college student now. You're always so reliable!!
Very good video! Super clear, shows all the important examples, in less than 10 minutes! Well done!
Thank you so much! Your 9 minutes and 25 seconds made more sense to me than an hour of self-tutoring!
thx dude !
I'm watching this form Saudi Arabia
Funny how a youtube channel from 2008 still helps students with both college and highschool cal. Mad respects
im near the end of my masters degree in university right now :)
A simple example based explanation. Thanks.
"It's almost so simple, it's hard" - Couldn't stop laughing.
Thanks for the great video.
SO helpful, thank you. You are a lifesaver.
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.
Exam in 6 hours, thank you so much.
@Shallowz987 i do not do online tutoring. i used to tutor in person but i am pretty much done with that too
you're a God send man, thank you!
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!
at 7:20, how do you know that 0 is between x^2 and tan(x)?
+idknuttin
And how you know that 1 + 0 + 0 + 2 = 3?
Are you kidding me?
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.
the range of tan(x) is all reals though
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.
I have a calculus exam in two hours and you literally just saved my ass. THANK YOU.
I LOVE YOU PATRICK
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
excellent videos, fast, well explained and very detailed... Good Job !!! thanks for the video
@rr5001 it is posted as a video response
You are the real St. Patrick....
2 days worth of class and confusion just got explained in 10mins. Gotta love youtube
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.
Dear Uncle Pat, thank you for single handedly giving me the knowledge to pass my calculus class. I hope the family is well.
1:10 ''it's almost so simple it's hard''
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.
so the derivative of an integral is just the integrand? thanks!
when ever i get confused with calculus chapters I directly go to ur clips and I get understood ......thnks 4 ur never-ending support
my case +1
Just brilliant! Do I even need to attend Engineering lectures anymore? Thanks for the tutorial.
WOOW MAN!!! YOUR KING. your 3mins worth of explaination was my teacher's week worth.
my exam is in 4.5 hours.... cramming much?
MrCtown8 yes!!!
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.
@@greatcanadianmoose3965 So? How did u do
@@johnfei434 No clue. I hope at least an 80
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
=)
I learned more in 10 minutes on TH-cam than 3 lectures in a row on this, thank you so much.
midterm tomorrow...after this video i don't think ive ever been this happy in my entire life . FINALLY i understand it !!! THANK YOU
thanks for the kind words : )
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?!
thanks for watching for so long :) glad i could help out a bit
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
"Good luck out there." I'll need it, thanks.
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 was stuck on my calc homework for over three hours. then if ound your video and i finished it in 20 minutes. thank youuu
Wow very clear explanations. Defenitely the best math tutor on TH-cam.
no problem!
This is one of the best , simple , and clear explanation for the fundamental theorem of calculus . Thanks for your effort.
The first minute of this video cleared up over days' worth of confusion. Concise explanations, thanks!
@jumpman111489 yea, it looks more confusing than it is!
Thats it...oh my god my professor kept giving us fresnal integrals like sin(x^2) and cos(e^x). I thought you need to take the integral and do top minus bottom but no one in the class knew how to integrate the functions LOL. Thanks to your video, I realize you don't even need to take the integral...THANK YOU!
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!
after one video, i am enlightened. THANK YOU SO MUCH.
never stop posting videos.
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 ,,,,
Dude...I LOVE YOU...You are 200 billion times better than any of the professors at my University!
Bro Patrick shout out from the University of Chicago. You're killing it.
bless your soul!! hopefully with this I won't fail my quiz tomorrow
@th30n1y0n3 no problem, happy to help!
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've been confused as hell in calc and you just summed up 2 class periods in one 9 min video. THANK YOU VERY MUCH!!