Fundamental Theorem of Calculus Part 1
ฝัง
- เผยแพร่เมื่อ 28 ก.ย. 2024
- This math video tutorial provides a basic introduction into the fundamental theorem of calculus part 1. It explains how to evaluate the derivative of the definite integral of a function f(t) using a simple process. f(x) is a continuous function on the closed interval [a, b] and F(x) is the antiderivative of f(x). You need to be familiar with the chain rule for derivatives. This video contains plenty of examples and practice problems.
Antiderivatives:
• Antiderivatives
Basic Integration Problems:
• Basic Integration Prob...
Indefinite Integral:
• Indefinite Integral
Definite Integral:
• Definite Integral
Differential Equations:
• Finding Particular Sol...
_______________________________
Properties of Definite Integrals:
• Properties of Definite...
Rectilinear Motion Problems:
• Rectilinear Motion Pro...
Sigma Notation - Calculus:
• Summation Formulas and...
Riemann Sums - Area:
• Riemann Sums - Left En...
The Midpoint Rule:
• Midpoint Rule & Rieman...
________________________________
Finding Area - Limit Definition:
• Finding The Area Using...
Definite Integrals - Geometry:
• Evaluating Definite In...
Fundamental Theorem - Part 1:
• Fundamental Theorem of...
Fundamental Theorem - Part 2:
• Fundamental Theorem of...
Net Change Theorem:
• Net Change Theorem - C...
__________________________________
Final Exams and Video Playlists:
www.video-tuto...
Full-Length Videos and Worksheets:
/ collections
![[TH] FS vs BME - VCT Ascension Pacific - Lower Bracket Final](http://i.ytimg.com/vi/wnygqsR2Fig/mqdefault.jpg)
Final Exams and Video Playlists: www.video-tutor.net/
Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections
Next Video: th-cam.com/video/ns8N1UuXl4w/w-d-xo.html
I swear this man does not get enough credit for everything he does. I love you Mr. Organic Chemistry Tutor Man ❤️.
th-cam.com/video/y_XwQkchwrE/w-d-xo.html
Thank you Jesus Christ for your existence. I’ve been trying to wrap my head around this theorem for two days now and every damn video was finding F’(x) instead of differentiating it. I WATCHED 23 videos before I came across this one. My proctor kept mentioning how the number doesn’t exist and I was like “😐wtf do u mean it doesn’t exist?” And then u just kept working them out and explaining them and then BOOM finally clicked. Gosh dang thank u so much.
lol
Billy Bob
f'(x) is a sedative this is anti deravative
th-cam.com/video/y_XwQkchwrE/w-d-xo.html
Teachers - 2 hours
OCT - 11.5 minutes, take it or leave
th-cam.com/video/y_XwQkchwrE/w-d-xo.html
And yet he still makes more sense than my teachers.
your name is cool
MISTER JIM HALPERT
legit spent HOURS. hours. fumbling around trying to understand the notes from class (and i take thorough notes!!). watched your video and it instantly made sense. you just go through it slowly and walk us through it all step by step. you don't skip steps like a lot of professors do, which helps SO so so so much. i can't thank you enough. seriously. thank you.
The first 3 minutes of this taught me more than 4 hour long calculus 2 lectures. Thank you so much. I've been trying to wrap my head around the idea of the variable switching from t to x, and you explained it very well.
Words are not enough to explain how thankful I am because of You. God bless you. May you prosper in all that you do.
I am actually pulling a better mark in my calculus than what I did in High school math because of you dude, you are genuinely a god-send!
If only my calc teacher was as concise, clear, and straightforward as you!
I can't thank you enough for releasing such great content! I will continue to watch your videos.
I just want to say...this guy is amazing!
th-cam.com/video/y_XwQkchwrE/w-d-xo.html
Your increasingly complicated examples are perfect way to explain this.
ur voice is so relaxing
Got a quiz coming next Wednesday and when I was in class, I was blank and couldn't understand but you just explain it so clear and simple, THANKS!!
Dude you are amazing you teach it so quick and it efficiently we don’t deserve you!
This video is the only reason I'm going to pass my Calc 1 final today
What is your name broo? You deserve all the praise there is..you are my teacher
Walter
Thank you about your efforts, you help me a lot, and I recommend you to my classmates from my college ( scince)❤️❤️
I cannot thank you enough. May God bless you.
Very thorough explanation! Thank you for the help!!!
Omggg thank you, I literally did not know what the hell was going on in class...thank you man thank youuuu
Forgot everything over the summer from AP Calc AB, great refresher for BC!
th-cam.com/video/y_XwQkchwrE/w-d-xo.html
thank you so much for your explaination i finally get it how its work
10:14
ah I see, the antiderivatives are taken similarly to other derivative rules, in the sense that they're defined only when the the input is solely x, as soon as we get anything else, we must use the chain rule to differentiate it.
got it thank u
YOU ARE A LIFE SAVER!!!!!!!!!!!!!!!!
Brilliant man! Really cool! What is the meaning of taking the derivative with respect to the bounds of the integral, in plain English? Is there an intuitive explanation?
I literally love you so much
Wow ... Really amazing . God bless u sir
Thank you so much brother 🙏🏽🙏🏽🙏🏽🙏🏽
very helpful video, thanks
Genius! The mysterious, laborious FTC2 is made like a breeze here, super fast and easy. Thank you for sharing this!
Unfortunately, this tool can not be applied to definite integral where antiderivative is required which disable this direct substitution wonder. Is this correct or not? I wish it is 'not'. :D
my professor is an amazing mathematician, but not a professor. they explain it in ways that make it more confusing
What’s the difference between x and t, what do they represent
Thank you very much ❤
Your video is sooo helpful. thank you so much. :)
Why there is a t variable in a given formula? what is the purpose of t ?
man thank you ! You saved me final exam !
You are not explaining why you need to to use the the chain rule for the bounds of integration.[ at least as I can "get it" ]. Is it because the bounds of integration are variables in terms of x and not just a constant?
Thank you!!
Why your soo good
This guy delivers the goods!
i got confused at 1:55 when you talked about t but said x
Why are you so wise ?
Can you help me to solve this one🙏
d/dx with the integral of sin (t^2) dt from 1 to x
...hope you can help me in solving this problem. Thank You
Thanks a lot sir!!!!!!
i love you bro 💞
7:40 but what about the (2x) along side f(x^2)? Do you just ignore that?
EDIT: nvm
Saved me fr fr
Great siirrr
At 7:27, why are you multiplying 2x?
edit: Oh nvm
I really wish I could reach through my screen and shake your hand. I learned more in this video in 5 minutes than a 2 hour lecture. You are a god-send to students. Keep up the good work!
th-cam.com/video/y_XwQkchwrE/w-d-xo.html
Your videos are very helpful. I dont know why some math teacher complicate things
@@imanemimi380 Some professors are great at solving math problems but they don’t know how to teach.
@@voodooblue6162 I feel like that's most of em...
@@B1SQ1T No
thank you !!
the reason this man teaches so well is because he stands in our shoes and looks at from our POV, professors refuse to ever do that. You've helped me pass chem. and calc., thanks a lot man!!
I swear OCT has been saving my ass for years now. I feel like you deserve a portion of my degree because of how much I've learned because of your videos. Seriously though, thank you.
What degree are you going for?
Lmaaaao he does actually deserve that
😆😆😆
Me: Hmm, the fundamental theorem of calculus, sounds important, better understand this.
Also me 24 minutes before the test
me 15 minutes before the test ; - ;
@@aryanahuja9709 during the test
@@thederpynarwhal4027 haha nice! Hope that went well lol
@@thederpynarwhal4027 After the test... 🥲
2 hrs before exam
so far OCT has carried me through Calculus 1, Physics mechanics, Chemistry for engineers, and Linear Algebra. Would not be making it through 1st year eng without you!
Same here. Carried through Calc I, Phys mechanics, and now carrying through calc II! Absolute W OCT.
Bro do you need a scholarship for all your work ?
ice goat yes !!
Yeah, I couldn't understand this in my 75 minute calculus class but it took me less than 15 minutes to get this.😀
@@laurynhillary6944 same
I got 95 /100 last semester and that’s all because of you . Respect ✊
This beats the 2 hour lecture I had from my professor who does nothing but read the textbook
I hate the textbook
With finals coming up I just wanna say thanks so much for all the help this semester you’re the reason I’m going to pass chemistry :D (and hopefully calculus but we’ll see)
did you end up passing calculus?
@@alexp5005 Passed Chem with a B but unfortunately I got a D in calc. I transferred schools and I’m taking it again but doing much better this time Lol
@@jolene7695 ayeeee what I like to hear! congrats on chem, and nice pfp
When you have 60 minutes and you have to complete 20 questions of this? all you need to learn here is the fastest way lol. thank you for your help
anything but the fastest way is a rip off
th-cam.com/video/y_XwQkchwrE/w-d-xo.html
who else here for ap tests
I am sooo grateful for your lectures, man. I am watching this video 10 minutes before my midterm, you saved my day!
I’m only 14 and I’ve learned so much calculus and trig from this guy and thanks to him I’m ahead of the curve and am doing much better in school.
Integrals at 14? Bro what school system are you even in? That's insane, you're like what grade 9? I'm doing integrals at 18 in university holy
i donk its their school i think theyre just interested
I'm pretty sure Asian schools do it at 13/14 js not so in-depth yet
@@BabaSphere
keep it up dude!
@@BabaSphere i mean i was doing them at 15 so im guessing they were in a similar system and wanted to get ahead of the class
🙏Feel instantly safer when I have to learn a concept and see you've created a video for it.
I watch these videos on 2x speed. That’s how little time I have bruh.
Sir Organic Chemistry Tutor, I salute you for posting informative videos. You have saved high school and college students from failing their calculus I am in high school taking AP Calculus. I learn more by watching your videos than my high school teacher. I humbly request you to please post videos of AP Calculus FRQ's solutions. There are few videos on TH-cam but you are undoubtedly the best calculus teacher on the net.
"That's terrible looking 2"😂
good lecture i think you Sir should come here in south africa
th-cam.com/video/y_XwQkchwrE/w-d-xo.html
@@kumarkumar-hy4hd can’t understand Indians
Bro, thank you SO much. My AP Calculus test is in a couple of hours and this is helping me!
I came here for clarification when I started doing this. I'm now back for revision for my calculus exam. I never cease to thank God for you!
Can't believe Im doing this at 2 am. Thank you so much for all your videos!!!
You have single handedly reduced the amount of stress I would have experienced in life dramatically. Thank you sir. Thank you.
Honestly, I love you so much. You're always spot on with your content. Every second in your videos is valuable. You're so much of a blessing ... 💖
Thank you for saving me literally hours and possibly my entire grade 🙏
WOW. My head had been spinning failing to grasp this from my lectures. You simplified everything!!! Thank you! You are heaven sent indeed!
th-cam.com/video/y_XwQkchwrE/w-d-xo.html
Thank you, your videos include very complete explanations and different levels of difficulty which is what make them worth it to watch and follow. And the pace and tone of voice are a plus 👏
i just watched a 2 hour lecture on this and i was so lost. But it finally makes sense now thank you!!!
Thank you so much. saving me rn
Why does F(0) = 0 at 3:02
organic chemistry teacher is literally every engineer's best freind
wow! thank you so much once again!!
Your teaching level is high
When I am in need I can always count on OCT to pull through, I wish you nothing but the best in life. Thank you so much for making complicated lessons seem so simple when you explain it. Also to the rest of my fellow scholars we got this, just keep push through it!!!
You are the king the one and only king
Till the second last example, I was really iffy and still confused. But, I tried the last example, and I got it! Thank you!
JFC thank you so much for this video. In the first four minutes I finally understood the lesson that my teacher spent 50 minutes
Thanks king!
I can’t really express my gratitude to you, I accidentally missed this lecture at my college and thought that I was screwed.
Explains the concept simply and succinctly in the first few minutes and gets straight to application and tons of problems to test your abilities. Perfect.
thankyou bro
You saved my life man, literally was so depressed trying to understand what I missed reviewing. I'm literally in upper-div courses and I feel like I never covered Calc1/2 properly. I really mean it, thank you.
Some times I get stuck between the idea that you might be an AI or a human...any ways tnx a lot
Literally none of this was in my college packet. We only went over part 2. Only a small gray section had a basic formula for part 1 but none of the problems actually went over it. I do the homework and lone behold the first fifteen problems are of this... like wtf. So much here that just simply wasn't taught.
lmao my teacher took 2 -3 days (1hr per day) to explain this !!!! and i still didn't understand it. Now within 6 min i understood every concept. Thanksssss!!!!!!!
The first min it’s easier to say that the integral g(x) has anti derivation G(x) and now by the theorem G’(x)=g(x). And if is composite function g(x) has anti derivative wich will be composite function G(f(x)) than the G’(f(x))•f’(x)=g(x). Chainrule.
Learnt more in this video than in my teacher's 2 hour lecture! Thank you
I very much like how these problems are solved using both fundamental theorems of calculus. The method sheds light on both theorems simultaneously. There is, however, a way to do these by using only part 1 of the fundamental theorem. Not as elucidating but doable and, afterall, theorems should have the power to stand on their own.
what happens when you differentiate the last problem again? For example, its finding a second deritative of a fundamental calculus questions.
hey at 7:11 are you saying the derivative of X^2 is (X^2)(2x)....? Just was a little confused on that part. Was that a mistake?