just do 1 integral, not 3! (Cauchy's Repeated Integral Formula)

Cauchy’s formula for repeated integration. I worked it out "backwards" from DI method.

blackpenredpen
math for fun

[blackpenredpen]

Btw guys.... I put in a lot of work in making this video too.... so, watch the math, too, yea?

Let's see if we can keep the ratio of (number of likes)/(number of views) to be > 10%

[DragonKidPlaysMC]

1. I am a grade 11 student who taught himself calculus through your videos. Back then, I saw Math as a unnecessary subject that just adds burden to students but you really changed my perspective. It made me cry a lot haha but the way you teach with such enthusiasm and happiness changed all of that.

Thank you for changing my perspective since there was a time that I felt really down. I tried self-harm and all that kinds of things before. And when I felt sad I would just solve a Math problem and that distracted me from thinking about how miserable I am. I would watch your videos and feel at ease and forget my problems. So thank you for doing these videos!

I really want to join the biggest Math Olympiad in our country but I feel like I’m not smart enough so I’m trying my best to learn as much math as I can to hopefully compete internationally which is my dream that I’m not sure if I can achieve.

2. I discovered your channel when I wanted to derive a closed formula for the nth fibonacci number. I asked my teachers if such formula exists but they didn’t know so I tried to derive such thing.

After trying my best, I gave up and just searched it in youtube lol. There was this other video which used power series and stuff like that which I didn’t understand since I didn’t know calculus yet. So I kept scrolling until I finally found your video deriving the formula. It was awesome! I remember being mesmerized with your enthusiasm. I looked at your other videos and when I saw your video regarding the square root of i and I was amazed by it. I was really shocked that such thing exist! And as far as I can remember that video made me subscribe to you and I have been watching every video ever since!

3. My new year goal would be to have a consistent learning schedule since I really want to learn so much things like Number Theory, Linear Algebra, Multivariable Calculus, Complex and Real Analysis so hopefully I can compete in that competition. It will happen next october so wish me luck!

4. If I can win that gift card, then I will buy any book regarding number theory or abstract algebra or any Math book! I don’t have any Math books so yeah. I really want to learn these kinds of things but I don’t have a mentor or a good teacher like you to teach me. So yeah thank you for all the videos you make. Thank you for making me love Mathematics!

#bprpXmas1

[BigLiftsITA]

7:21 this kind of excitement is what makes your videos amazing

[blackpenredpen]

Hi all! The giftaway is now over. I will announce the winners this Wednesday.

[weinboyz]

1) I am a high school senior/ Calculus B/C student that cannot tutor pre-algebra for the life of me
2) I discovered your channel while watching numberphile and saw you on reccomended (this was when I was in pre calculus). I started watching your videos and picking up on how to do calculus. I had no clue of what was going on at first but just thought it was so mesmerizing what you were doing and how amazing it was. That’s what made me subscribe and keep watching.
3) My biggest goal next year is to get to a +9 handicap in golf (I am a golfer and am trying to get a lot better)
4) with the new e-card I would probably buy some new red pencils, erasers, and markers for my paper and board that I use for teaching.

[leonardoalanis]

Well, let's see #bprpXmas1
1. I am an Engineering Physics student at ITESM in Mexico, and I'll be in the middle of my sophomore year next semester.
2. I discovered your channel on the recommended section after just after I discovered Grant Sanderson's channel. What made me subscribe is that I believe that in your channel I learn some useful tricks, tips, and problems that I'd never have seen or practice If I had just stayed with my course material; in fact, the 100 Integral document and video helped me a lot to improve my skills in integration and gave me some advantage over my classmates in Calculus III and Differential Equations
3. My biggest new year goal is to survive in Real Analysis next semester. I'm taking that course as an optative course in my studies.
4. If I won an eGift Card, I'd buy a math or physics books, they are quite rare to find in Mexican shops, the only way is through Amazon.

[mattapo]

1. I love everything to do with space
2. I discovered your channel by looking for ways to do integrals
3. I want to get into Engineering in my university as my goal
4. Im not too sure what I would buy yet for myself.
You're awesome!!

[Close]

#bprbXmas1
1. I am a 3rd year student at the Wrocław University of Science and Technology. My field of study is Cybersecurity, but I am in love in math even if I do not have it anymore I still want to learn new stuff.
2. When I was at my first year I started to search useful informations and I bumped into your channel. I said to myself that "This guy is awesome, I think I can learn a lot about math and a different approach to it."
3. I want to make an huge math/cryptography app (1st version to pass the project and 2nd bigger version just to satisfy myself)
4. Probably something to myself and my fiancee, I don't know yet :P

[simponic]

#bprpXmas1
1. I'm 16 and in my 2nd year pursuing a bachelor's in Applied Mathematics
2. I discovered your channel while watching some MIT Integration Bee videos. When I saw your amazing techniques and simple solutions, I subscribed.
3. My biggest new year (and new decade) goal is to finish college and get a job.
4. If I win I'd get some nice Full-touch chalk.


Thanks!

[chubbybunny]

1) I'm a 22 year-old student who lives in Florida and is dual-majoring in Math and Physics.
2) I found one of your videos in the sidebar while watching the LetsSolveMathProblems youtube channel. I ended up subscribing because I like learning new tricks to solving math problems and it seems like you're full of them.
3) At the moment my new year goal is to have taught myself Abstract Algebra by the beginning of the Spring semester. I ended up having to drop the class because of some brain problems I've been having recently. It's been making it kind of difficult to learn things in classroom settings, so I want to teach myself before the next semester so that I'll have an easier time with it when I take it next.
4) I normally do my book shopping on there, so It would end up going towards expanding my library.


#bprpXmas1

[Wyldina]

#bprpXmas1
1. I'm B.Sc in physics and B.Eng in electrical engineering
2. Random suggestion from Youtube, and your skills, tricks and enthusiasm made me subscribe
3. Keep my weight down below 100 kg
4. I have absolutely no idea! ^_^

[madtasmo]

1- I'm a 16 yrs old student, and I'm really into maths (obvsly), physics and programming.
2- When I was trying to brush off my integral calc skills, the yt algo worked its magic and recommended me your channel, and oh boy, right after finishing one of your 100 integrals video I slammed that sub button as hard as I could.
3- I've never done one of these resolutions, but I guess I'd love to advance in some online (advanced) physics and maths courses.
4- Buy a (physics) book that I've been dying to get my hands on!

[Angel_Sony]

1) I am from Argentina, my english is not perfect but I understand and enjoy the math! My favourite math book is 'Matemagia' from Adrian Paenza. A famous mathematician from my country. I'm also a pianist.

2)Youtube recomended me this chanel after seeing videos from 'derivando' and 'Eddie woo'. I preffer your channel because you explain every single detail.

3) The goal is going to gym more ofthen. I'm 20 so when I stopped growing up I started to grow to the side.

4)To be honest, a videogame. Argentina's money got devaluated to buying anything in dollars became expensive.

I just wanted to tell. I love your channel! I just started to do integrals in college and every single teorema and demonstration is so good. Math is so perfect! Your videos helped me a lot with my previous exam... last week~ ♥️

[mcaidanwolf]

#bprpXmas1

1. You helped me learn Calculus. I watched your videos without knowing any Calculus and started to piece together what you were doing.
2. I came across your channel when I started to look ahead after being bored out of my mind in my freshman Algebra 2 class. I found the content to be interesting and the more I watched, I more I became interested in higher level Mathematics (even if I didn't know what an integral was at the time).
3. As this is the last year of IB Math HL 2 in the IB curriculum, I'm aiming to pass the IB exam with at least a 5 and get a 16 or higher on my IA.
4. I feel as if I owe one of my best friends a math gift. So, I'll get one for him.

Keep up your hard work BPRP, you make math fun.

[Vishal-jzbb]

#bprpXmas 1
1. I'm a student of class 12 and i like to learn new things
2 . I discover this channel when I'm looking for Ramanujan series (sum =-1/12).
3 . I want to perform outstanding in upcoming exams and to do something special for my family
4. I will purchase some study material for physics as I'm weak in physics and when my goal is achieved i will give this material to my juniors in school

[DebarghyaBasak_hi_every_one]

#bprpXmas1
1. Rather than wanting to know just how we can answer a maths problem, I also like to know why the answer we get is the answer: how it fits in the greater scheme of things!(I love to take the derivative of an integral I just solved and plot the function and see what kind of an area it bounds)
2. Integral videos obviously! Was searching google for the integrals I couldn't solve and your videos came up! And I had to subscribe when I saw your regularly upload integral vidoes!
3. To clear the IIT-JEE(the Indian engineering entrance exam) exams coming up and get a good rank so that I can join a good college and pursue either physics or maths.
4. I wanted to buy a book called Gödel Escher Bach by Douglas Hofstadter, a book on maths art and music and why and how they are related. The book is on the expensive side 10$+ and the gift card will really help me get it!(And a few other books on physics too!)
P.S.: I was introduced to Dr. Peyam's channel through your videos, so a big thank you for that too!

[pr_kp]

1. You’ve helped me understand harder parts of calculus in a super intuitive way.
2. I was looking up AMC and AIME problems and your channel popped up out of it.
3. Make the AIME! :). I would be really happy if my practicing on AMC 10’s finally paid off. After that my goal would be to manage time better, because I use my time less efficiently than most.
4. I’d probably buy a stuffed animal and gifts for my friends and family. Maybe I’d buy a metronome for my instrument, or I even might get a few books.

[koolaid]

#bprbXmas1
1. I can read minds. I am a mentalist.
2. Preparation for IMO.
3. To be the world topper for my country in IMO.
4.Tons of books for IMO.

IMO i am coming.

[HenrySchach]

#bprpXmas1 1) Why are you watching videos of blackpenredpen? 2) One of your videos was recommended while I watched German math videos. 3) I would continue my study in Physics and improve my math skills. 4) I would buy a book related to my study

[EdwardTrain]

@
1. I went to a cool google cloud summit a season ago
2. I found your channel through a maths teacher and subscribed because I wanted to discover cool things about maths
3. learn morse code, I felt like it would be challenging but fun as I could improve my hearing memory and instincts
4. morse code transmitter and a receiver

thanks for making me interested in maths lol