Calculus 1 Lecture 4.1: An Introduction to the Indefinite Integral

Calculus 1 Lecture 4.1: An Introduction to the Indefinite Integral

[@sciencesimplified3890]

You’ll love this story. I dropped out of my first year of college with terrible grades.. I took 4-5 years off and worked as a dish washer.. I eventually decided to give school another try, however was worried because I had forgotten EVERYTHING I learned in high school. However, I woke up each morning at 6:30AM and watched your lectures for hours and hours and eventually received As in both calculus I and II, graduated magma cum laude in neuroscience, did well on my MCAT, got accepted into medical school, and will start my medical residency in July.. Your videos genuinely helped give me a free resource that allowed me a second opportunity at success. I have no idea why these videos popped up in my feed all these years later but seeing your channel is so nostalgic

[@istoleyourwalletwhileyouwe4717]

Good story very inspiring. God bless currently a freshman trying to graduate in 2.5 years using professor leonard to get ahead and supplement my journey

[@sciencesimplified3890]

Wake up early and study consistently daily with no exceptions, just make it a non negotiable component of your routine and your efforts will be appreciated @@istoleyourwalletwhileyouwe4717

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Nice work! 🎉

[@dyln8141]

reading this inspired me, do you have any advice on doing well in school? *I'm a freshmen in uni, about to take gen chem, physics, calc 2 next semester, and I'm worried.*

[@istoleyourwalletwhileyouwe4717]

@@dyln8141 damn bruh what you studying😭

[@darthboganis1356]

Rectangle Method of Area under the curve 1:50 Anti-derivative Method 11:20 Finding formula for area from f(x) EXAMPLE 19:00 Area under the curve EXAMPLE 2 26:15 Indefinite Integral 42:00 Basic Integration Table 1:00:20 Properties of Integrals 1:25:15 - The constant, C 1:27:40 - trig function problem 1:42:20 - algebraic manipulation 1:46:20 - Undoing a derivative gives you the integral 1:53:45 Equation of the curve for a specific constant, C 1:55:50 Introduction to Differential Equations, initial value problem 2:00:00 Initial value problem Example 2 2:14:00 Anti-derivative problem 2:17:00

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you're doing the lords work

[@darthboganis1356]

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[@Daniel-yt7fm]

Thanks!

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the hero we needed

[@kristinerabideau860]

Professor Leonard, I can't thank you enough for the help you have given me in algebra and calculus. I returned to school in engineering after 15 years at the age of 46 and your online classes have saved my butt. When I graduate, you will be invited to my graduation, since every one of my professors should be there. Thank you so much. ~ Kristine, Windsor ON Canada

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This, except me, right now, doing a masters in statistics.

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Lol. Cpa and lawyer. Thinking of getting a similar degree just to prove I can. These videos have helped tremendously if only we had all this in the 80s, yes that’s how old I am.

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I'm on the same path but I'm aiming for Computer Science, he made me realize I'm not dumb after so many failed attempts at higher level mathematics years back.

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@@EliseLogan Stats gang! Just started my MS in Biostats

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My favorite part about this lecture series is that one guy who laughs at everything you say.

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he is in love

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@Jackson Kagy that is very rude and disrespectful.

[@staticsnipezs1819]

dude i used to laugh at everything my math teacher said when i was in 5th and 6th grade. it was so weird

[@arthur38379]

@Knox Adan why did u come to a calculus video to say this?

[@HaIsKuL]

Integration Table at 1:15:38 if anyone needs to keep going back to it.

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[@theguildofsilence]

fucking actually same

[@gablol975]

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[@joshmick]

Then stop going to college dummy

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Still go to college

[@cocowood2316]

Ive stopped going to class because these videos make so much more sense to me. Thanks for the A's brother

[@pockydust3404]

I enrolled in an online calculus course and I literally don't read any of the content anymore. I just read the title and look for the content with Professor Leonard. So far I'm getting A's!

[@andranik70]

Indefinite Integral starts at 41:00 And thank you for the videos!

[@SatishNatarajan]

Yeah, but the first 41 minutes is very important to understand what an integral/anti-derivative is.

[@dude10432]

Thank you omg

[@cornelxbox25]

The student added 256 instead of -256 and got the wrong height (784 ft). To help with the +c dilemma; remember that there is always a constant in your function. y=2x^2 has a constant and it is +0; we just don't write the invisible 0 for the same reason we don't write powers of 1 or multiplications/divisions of 1 (it's redudant).

[@alonsoaravena6209]

This should be higher up. I think they forgot that the first component is: negative 16 * (t squared) As opposed to (negative 16*t) squared I try to use extra parentheses all the time to not forget this

[@mended8774]

thank you for saying this i thought i messed something up

[@AlexanderChilds]

Absolutely magic. When I was in High School, I stopped taking Math at Algebra 2 because I had enough credits to have a free period or two in my senior year. Big mistake. I chose Computer Science Major in University and hadn't had any classes in almost 20 years. That said, I jumped-in anyway. With the introduction of Calculus, your videos have made things so much easier for me to understand than just reading from a text book (online courses for me due to my job). Just started Integrals today, and when you put the area function on the board, I immediately saw the derivative and really, my mind was blown. I really enjoy watching your videos and they now come highly recommended to my classmates, coworkers and friends as it breaks the concepts down and drills them into your head. If you asked me in High School if I'd ever take Calc, I'd have said, "Fat chance. Too complicated." You've broken that idea for me. Thank you!

[@Leo3ABPgamingTV]

An easy way to memorize whether you should put negative/positive sign for cos/sin when you integrate/derivate is following the clock direction on unit circle with cos/sin axis, so when you derivate you move clockwise (from sin ---> cos---> -sin ---> -cos and then back to sin), when integrate you move counterclockwise (sin ----> -cos ----> -sin ----> cos and then back to sin again). Hope that helps

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I know this is 3 years later, but no worries! I have copies backed up just in case.

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[@ethan073]

I was nervous going into it, but I've really enjoyed Calc 1 this semester and I am holding onto an A in the class-your videos are definitely a big reason why! Thank you!

[@agh1750]

I mean this in the best way possible, you teach calculus in such a way that even a person with an IQ of 70 could understand, that is, anyone who can learn to speak a language could learn something as complex as calculus when taught this way. That's not to say you teach it at a low level, rather, you minimize the abstractness by introducing concepts and notations concretely through worked examples meanwhile gradually introducing more abstract ideas before ultimately explaining the general mathematical theorems in all their glory. I've never seen such thorough and comprehensive instruction, you manage to do all this without introducing any inaccuracies as well which is amazing. For someone learning calculus 1 or 2 for the first time, my recommendation would be to first read the book "Calculus for Dummies", then watch Eddie Woo's entire playlist for initial exposure at a high school level, followed by Professor Leonard's videos, and finally the MIT's playlist of video lectures on single variable calculus. The final step would be to pick up an actual calculus textbook, read through all the pages and work through all the problems. All this can be done in the span of one summer prior to taking a calculus course at university. If you do everything I said before actually taking the course in person, you'll be able to follow everything in lectures while asking meaningful questions from your professor in person. Even a moron could pass this way.

[@stannissama3819]

Which calculus book would you recommend?

[@agh1750]

@@stannissama3819 Stewart early transcendentals

[@stannissama3819]

@@agh1750 Thanks. Definitely will look into it.

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thank you I will definitely read that book in my summer holiday

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You are amazing , professor. People like makes the world better place, because you share with us something priceless - knowledge. And you don't just spit it out like most of the lectors - take this, do this and this is the result. You are explaining by the way, which is fascinating and understandable - which is the most important. People like you can make the majority of students to really understand math. Thank you from the distant Bulgaria and thanks in advantage for the exam that I will pass excellent, I hope, because of YOU. Be well, healthy and blessed, Professor Leonard.

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+Professor Leonard. Really appreciate the videos you make. I'm currently in Calculus 2 in college and finding my teachers very knowledgable on the subject but can't teach the subject very well in a class setting. I went back to the basics in a lot of my cal 1 to brush up and even taking calculus 1 a year ago the videos you provide in details are great like the back story and the true reason behind why we integrate and take the derivative because i was never taught them. I never fully grasp the concepts of Integration until this video so keep doing what you do you're an awesome teacher!

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[@roa1437]

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[@kratosthedude]

2:42:30 It's not 784ft, -16 (4)^2 + 128 (4) + 16 = 272ft

[@kratosthedude]

Correction @ 2:44:30

[@leavethematrix9939]

Bilal Raja yes he forgot the "-"

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Bilal Raja This makes me so excited for the spring semester when I do take calc. LOL.

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Your quick but intuitive explanation/proof, that a(x)=a'(x) really helped me wrap my mind around this concept. Before hand just seeing a(x)=a'(x) I couldn't possibly see why, but now I understand. Thank you!

[@alexhampton9719]

Amazing video! I read the chapter in my book about indefinite integrals and didn't even understand the purpose of anti-derivatives. This lecture is so well done. Great job! It's a pleasure to watch these lectures.

[@thedebis]

I was going to wait till the end of the playlist before I commented unlike your precalc video. But Professor the catapult exercise has to be my favorite from Calculus 1!! So far thank you!!!

[@xrisku]

272 ft high. your students dropped the negative sign on the first term. did anyone get a final answer for when it will land on the ground? if you set the position function to zero, you get: 0 = -16t^2 + 128t + 16. factor out -16, that gives you: 0 = t^2 - 8t - 1 that is nasty and equals -0.123 and 8.123 seconds. you would obviously toss the negative. you can only solve it using the quadratic formula, which is particularly painful. Just curious.

[@NozaOz]

Yeah I got the same, was hoping someone else wanted to know

[@SteamPunkLV]

wow I did this in my head and got 272 too, I'm so proud of myself

[@ayushdutta6511]

272 ft

[@mustafarizvi4275]

to find out when it hits the ground you will have to set the position function to -16 since the launch was 16 feet above the ground. you ll have to solve for -16t^2 + 128t + 16 = -16 which gets you t=8 and t=0

[@1eV]

@@mustafarizvi4275 no. The initial value will do the job for you here as we've included it already. You will have to set position to 0. And t=8.123s

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A knowledgeable and hot professor

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you have taught me more in the last 3 hours then my professor this entire semester really wish I had found you sooner than the night before my final.

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Then stop going to college dummy

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this man is just amazing. i wish he taught me calculus at university

[@marathondude]

IMO the pacing and explanation were good. Explanation clear, but deliberate enough that the viewer had time to digest the information and follow along. Appreciated that the prof made sure that there were several examples of how to arrive at anti-derivative. Well done, IMO. Plus sound level was good, other videos have prof talking too fast in a room that has too many echoes. Even if they know the subject, the video prevents student from hearing it. Good work.

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did you make it?

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love you man. love you so much. i can't explain how thankful i am... your videos helped me to learn integration, in 3 hours, what my previous teachers couldn't do it in 3 years...

[@jerrymahone335]

if you are wondering why 6 became 6X. it was always 6X but it was like this 6X^0. any number with a zero power is 1, and (1) (6) = 6. any number with a power of 1 is that number 6X^1. 6X^1 = 6X. You usually think of powers until squares (X^2), but ^0 and ^1 are there. you can have only one constant because C is where a slope crosses the Y axis or the imaginary plain.

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You did blow my mind many a time during the lecture. Thanks a lot.

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[@Peter_1986]

I have already finished Calculus 1, Calculus 2 and Calculus 3, but I am still currently watching literally every single video for those courses with Professor Leonard, lol. I have forgotten a lot of this stuff, and several of my current courses have Calculus 3 as a prerequisite (like Dynamics and Continuum Mechanics, for example).

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i have never understood the concept of s= ut + 1/2at^2 until today

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Professor Leonard, Thank you so much. I hope there more professors like you. The topics were difficult but made easy: in a way that every topic is not overwhelming and easy to digest. and of course, more examples. But what I really appreciated is how you tried your best and made every lecture exciting. hyping it up really helps. Thank you so much. please live a long, happy and healthy life with your lovely family so that you may continue to educate more students. This is really the best. Most importantly, it is free.

[@havakanable]

I wanted to thank you for posting this videos

[@silcalderale]

There's always someone caughing (since lecture 1.1)...I wonder if it's always the same! lol Great lectures by the way!!!

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7 years later and this is the only reason I have not killed myself yet

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Mr. Leonard is the Superman of calculus 🙏

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Wow! I didn't know Superman taught Calculus.

[@admiraloverdone]

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[@Ohm_Sharma]

At 2:42:18, the answer is 272 ft. 784 ft is not correct.

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i have midterm in 24 hours. my job as a reservist called me to work everyday for the last two weeks... I missed 6 lectures for applied calc 1. this guy right here is saving my ass. currently WIRED off coffee about to endeavor in the next 4 videos. SKO MARINE CORPS

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Watching in 2020, this is amazing, I wish I had found this sooner. He explains everything really well

[@davidx5828]

Finding the position function was amazing, I’ve always wondered how those come about. I have a budding love for math. Thanks Professor Leonard! P.S. I used to hate it.

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In India we have no proper professor at present to teach us. Thank you so much for giving sthese lectures sir.

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The best Indian teacher I know of is definitely Salman Khan on Khan Academy.

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you are the best

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I think the boy that sneeze and cough in every video has allergies to calculus THaNK YOU FOR THIS AMAZING LECTURE 2021 SENIOR

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Thank you so much, you are the only reason why I'm being able to learn calculus!

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You are so awesome Prof. Leonard. Your lecture video might be lengthy, but you give me the reason to watch them. Thank you once again

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I came here to refresh calculus I for calculus II and I'm wondering if I can find the rate of change for this man's work out routine.

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Professor Leonard is so engaging, that I keep pausing his video, raise hand, and ask question. lol

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Math genius by day Superman by night.

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The catapult problem illustrated and brought together a ton of great stuff.

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Your classes are very good. But I have problem recognizing the board.

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bruh you are ripped! And an amazing teacher!

[@MrYellowpower]

I've had 2 lectures so far in my calc 2 class, and I watched the first 5 mins of this video then suddenly i understand what was going on in the last 2 lectures that I was confused about. IDK HOW YOU DO IT BUT YOU SHOULD BE MAKING INSTRUCTIONALS FOR INSTRUCTORS

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Im taking calc as a student who doesn't do well in school. Im passing with an A because of these videos.

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Just aced Calculus. Thank you Leonard! Edit: will be using your videos again for statistics. that class doesn't stand a chance.

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[@formalPirateClips]

My mind was blown with the a’(x)=f(x) at 15:00. Math is sooooo cool!!

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I am confused. The integral of secx is ln|sex+tanx|+c, isn't?

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Do a tutorial on how to bench press 315 next.

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The only thing missed in his lecture is subtitles except it best teacher of math ❤❤