@@blackpenredpenHey bprp.if may ask, has there been any calculus question that you've personally created that had proved quite challenging for you to solve, ever before.
@@ryanspivey1819 Bro its impressive because he was doing it for 9 hours straight. By your logic, David Goggins doing 4030 pull-ups in 17 hours is not impressive either because there are teenagers who have done over 5000 pull-ups in their lifetime.
It is very refreshing to see the presenter to do things live, in real-time, with small typos corrected and elements of improvisation : that is exactly how these topics must be taught to any student body, not via a power point presentation :)
@@cameroncurtis7261it’s because they’re getting rid of blackboards. And if they still have blackboards they clean them with some chemical that makes it harder to see the chalk.
Can we all stand up together for a moment and appreciate how much hard work and effort bprp is putting into the hard and intricate mathematical theorems to make them easier? Cheers Steve, you're making my approach to calculus and maths for university exams easier! :)
I skipped ahead to see how badly your cheerful demeanour would be eroded after 9 hours of integrals, but you seem to be in great spirits throughout! Amazing! Also, you helped me remember how to do chain rule integration which I haven’t had to do in years, so thanks!
must say he is one of the best mathematics teacher i have ever seen [ he gives better pov to understand the question and solve it ] ...love from india 🇮🇳
calculus problems involve a lot of logic you learn in previous courses, in calculus you learn many laws and methods to solve specific problems and once you apply a rule that you learned, the rest is factoring and solving and stuff
You understand it slightly because you are just getting the style of it. Not knowing the logic behind will not help. But even understanding a bit without knowledge is good. I can see a good calculus student in you
Timestamps (Powered by Merlin AI) 00:02 - Integration techniques covered in part 2 03:00 - Derivation of triple angle identity for sine 10:26 - Integration techniques and special integrals explained 14:02 - Integration by parts involves differentiating and integrating functions in a specific way. 20:47 - Using different substitution methods for integration. 24:37 - Integrating a complex square root fraction using a substitution method. 31:45 - Pairing up sine and cosine for integrals 35:07 - The integral of sine X plus cosine X is x minus Ln absolute value of sine X plus cosine X 41:54 - Integration of secant times tangent, and using trigonometric identities for simplification 45:37 - Integrating 1 over 7 - 6x - x^2 using partial fractions 52:38 - Using power reduction formula for sine squared 56:11 - Integrating trigonometric functions and exponential functions 1:03:46 - Techniques of integration involving substitution and trigonometric identities. 1:07:58 - Integrating 100 differentials with trigonometric identities 1:15:53 - Integrating complex trigonometric functions and inverse trigonometric functions 1:19:21 - Integrating square root and 1 + square root of x 1:26:22 - Key integrals reduction formula explained 1:30:05 - Integral transformation using power reduction 1:37:32 - Deriving reduction formula for integrating tangent functions 1:41:44 - Explaining integration using reduction formula 1:49:38 - Discussing reduction formula for integrals of secant 1:53:28 - Integration by simplifying complex fractions 2:00:58 - Integration techniques and approaches focus over domain restrictions. 2:04:30 - Explaining the integral of cosecant 2x and its significance. 2:13:45 - Derivation of sine and cosine using half angle substitution 2:17:39 - Using trigonometric identities to simplify the integral 2:26:09 - Integrating complex trigonometric expressions using substitution 2:30:02 - Integration using trigonometric substitutions 2:39:38 - Integrating complex fractions with shortcuts and simplifications. 2:43:28 - Integrating complex expressions using trigonometric substitutions 2:51:55 - Finding the integral of e to the x times sine x plus cosine x 2:55:36 - Integration by parts technique for solving integrals 3:04:12 - Integrating inverse sine x over inverse cosine x 3:08:01 - Explanation of elliptic integral of the first kind 3:16:23 - Solving integral using error function and special functions 3:20:37 - Integration using logarithmic integral poly logarithm 3:28:46 - Integrating sine of (1 + e^x) using angle addition formula. 3:33:39 - Exploring integration techniques 3:43:13 - Integration of 1/inv sin X follows a similar pattern as previous problems. 3:47:49 - Integration using trigonometric identities 3:56:02 - Exploring the integral of square root of inverse sine X 4:00:44 - Integration of e^(x^2) and e^x/(1+e^x) 4:08:49 - Integrating special functions and using substitution to simplify 4:12:54 - Integration by parts used to integrate sine functions. 4:21:34 - Integration by parts with exponential functions 4:25:32 - Finding the value of p for the integral 1 / x^p 4:33:41 - Understanding the convergence and divergence of integrals. 4:37:40 - Introducing the concept of polar coordinates and change of variables in double integrals 4:44:57 - Understanding polar coordinates integration 4:49:01 - Explaining the Gaussian integral with polar coordinates 4:57:00 - Integral of e to the x from 0 to 1 is equal to the integral of e to the x from negative infinity to 0. 5:01:16 - Understanding negative integral values 5:09:50 - Understanding and solving improper integrals 5:14:18 - Using power series for integration 5:22:08 - Deriving and solving the integral for x to the power of t 5:26:01 - Using innovative substitution techniques for integrals 5:34:56 - Integration using substitution and limits 5:39:08 - The integrals are shown to have the same value through a series of manipulations. 5:47:50 - Simplifying the integral using factorization 5:51:48 - Integrating art functions which converge to zero 6:00:34 - Laplace transform explained with examples 6:04:22 - Using Laplace Transform to find an integral 6:12:13 - Explaining the integral of sin^3(x)/x^3 over 0 to Infinity 6:16:59 - Applying power reduction formula to simplify the integral. 6:26:03 - Derivation of I double Prime of T 6:30:47 - Deriving the integral of a specified function 6:34:03 - Graphing equations of a line 6:34:33 - Integration of sine X over X 6:35:36 - Utilizing substitution to solve integrals 6:36:07 - Integrating cosine of Y to the third power 6:37:10 - Integration involving tangent and secant functions 6:37:40 - Discussing integration method by changing variable to ln of Y plus 1 6:38:48 - Understanding the change of variable during integration. 6:39:22 - Integration using change of variable method 6:40:29 - Comparison between DY first and DX first for integration 6:41:01 - Integrals and region boundaries 6:42:04 - Calculation of Jacobian for integral transformation 6:42:36 - Understanding the integral transformation process 6:43:40 - Solving for X and Y in terms of U and V using Jacobian 6:44:11 - Integrating x squared plus y squared using absolute value and U substitution 6:45:15 - Understanding vertex coordinates and equations of lines 6:45:47 - Integration of U^2 * sin^2(V) over specified limits 6:46:59 - Integration over a quarter circle region 6:47:30 - Double integral of square root of 1 + y^2 over a triangle region 6:48:32 - Integrating infinite series pattern 6:49:02 - Simplifying the integral using series and summation
your way of explanation is so amazing!!, even though i didn't learn power series, i was able to understand the last question. your students are really lucky to have you as their teacher!
I really enjoy mathematics when I see the explanations so perfect that you do, thank you professor for teaching us and showing us your passion for this beautiful science!!!!
just found this channel and man as a 15 yr old entering his senior phase(where math gets real), I'm honestly excited after I've seen the dedication and expertise this man demonstrated. SO I hope ill be back in the next year or so actually understanding these concepts in sense.
All the best! Calculus is a fun experience, although frustrating at times. I hope you get to enjoy the subject as you go through this new phase of life
@@divinebanana8400 no not sure about that, i believe calculus comes in a later grade but not grade 10, calculus is near the end of high school for me (not so sure tho) but prolly more indepth in university.
Hi blackpenredpen, love the effort into these videos! I recently realized I have a family member who is also a professor at UC Berkeley! He is in the physics department, Rene Bilodeau. Small world. Happy new year from Canada.
hey BPRP, I just wanted to say how much I appreciate the content that you make and the incredible amount of work you put into it. you seriously have no idea just how much this content means to us and has helped us. I’ve been watching you since my first calculus class, and I have surpassed linear algebra largely thanks to the fundamental ideas that you have highlighted and reinforced in your content. thank you from the bottom of my heart.
if Q9 with the numerator and denominator dividing on cos²x, that would lead to dtanx/(1+tanx)² and a way for Q33 with multiplying 1-cosx up and down after decomposing the term sin2x in the denominator brings in (1-cosx)/sin³x as the integrand and results in c+[cscx(cscx-cotx)+ln|cscx-cotx|]/4 and Q35, c-2ln|cos(x/2)|; with the result of Q54, the x² term can be further operated; Q94, the result written down misleaded, π/2
Hello ! I hope you see my comment I saw this nice question so that I recommend it The question is : solve the system of equations a = exp (a) . cos (b) b = exp (a) . sin (b) It can be nicely solved by using Lambert W function after letting z = a + ib Hope you the best ... your loyal fan from Syria
I found an interesting approach to Q49. I added an integral of 1/lnx dx and also subtract it to keep the original value. Then I used IBP on the integral -1/lnx and I got -x/lnx - the original integral, so they cancel nicely. Then i just solve the remaining integral as li(x), so I got my final answer: li(x) - x/lnx +C
Watching this without even knwing what the fuck hes talking about is so relaxing bro. Im just sittin here watching an asian guy doin math and its so chilling ❤
An integral you should try: 1/ln(1/ln(x)) or -1/ln(ln(x)). It's quite a special integral. I also want to see how you are going to do it, since maybe the way I did it isn't the best. Btw. love your videos, keep it up!
I am watching this video for 9 hours as a review for an 1.5hr midterm exam tomorrow :) Learned many new techniques, which I wish I could recall tomorrow.
wow thanks i'm actually in the 7h and i so tired but it really fun doing it nonstop with you i swear, it really unfortunate that i didn't discover you before you really an inspiration and it was really fun doing it in one take with you, i'm looking to become better than you so don't give up on your perfect work and inspire people. thanks god there is some amazing teacher like you.
i didn't believe it at first so I dragged the track to speed up, and the first thing I saw was the clock turning smoothly. Respect. And thank you I needed this for calc 2
This is insanely awesome lmao it makes me want to go sit down and just practice along for as long as I can. This is such a great way to keep integration sharp.
Number 9)multiply nominator and denominator with sec^2x so we get integral of sec^2x/(tanx+1)^2 dx substitue u=tanx+1 Du=sec^2x so we get - 1/tanx+1 rewrite tanx as sinx/cosx, do the calculating and you end up with sinx/sinx+cosx +constant (sorry for my bad english)
Would u mind telling me how to reach sinx/ sinx + cosx using this way? I tried manipulating -1/1+tanx but couldn't find how yo reach it, but you inspired me by multiplying by csc² which will end up in a nicer way
OMG! It was really challenging. But thanks for such a technical solution. This guy is really genius and intellectual. Enjoying the content of this channel.. Well done keep it up. #SUPERMATHS
One error I noticed - 4:39 --> sinx * (-2sin^2x) = -2sin^3x not -3sin^3x Other than that great video! Keep up the great work you got me through all of Cal!
This is just so incredible and amazing! Also, I would love to see like some sort of competition in this between maybe you and Dr. Peyam or something like that (Maybe something like the MIT Integration challenge thing, but I'm sure you guys would make it more fun), You guys could put a prize on it too! I'm sure it would drive a lot of viewers and be much fun!
Timestamps below, all errors are my own :) the times below cut off some of bprp's best jokes/explanations/tired monologues, so watch those too!
Q1, 0:00:46
Q2, 0:03:03
Q3, 0:08:23
Q4, 0:12:34
Q5, 0:17:02
Q6, 0:19:42
Q7, 0:30:07
Q8, 0:33:45
Q9, 0:37:58
Q10, 0:45:16
Q11, 0:48:30
Q12, 0:53:16
Q13, 0:59:06
Q14, 0:58:34
Q15, 1:00:41
Q16, 1:04:56
Q17, 1:07:27
Q18, 1:12:27
Q19, 1:14:42
Q20, 1:18:50
Q21, 1:22:30
Q22, 1:25:14
Q23, 1:27:40
Q24, 1:37:44
Q25, 1:42:58
Q26, 1:52:14
Q27, 1:54:45
Q28, 1:57:45
Q29, 2:01:49
Q30, 2:04:49
Q31, 2:24:38
Q32, 2:27:17
Q33, 2:31:25
Q34, 2:35:00
Q35, 2:37:20
Q36, 2:42:02
Q37, 2:44:24
Q38, 2:50:18
Q39, 2:51:53
Q40, 2:56:12
Q41, 3:00:21
Q42, 3:04:07
Q43, 3:06:45
Q44, 3:11:58
Q45, 3:19:02
Q46, 3:24:19
Q47, 3:28:36
Q48, 3:31:54
Q49, 3:33:44
Q50, 3:43:40
Q51, 3:49:16
Q52, 3:55:44
Q53, 3:59:50
Q54, 4:03:18
Q55, 4:08:21
Q56, 4:09:21
Q57, 4:10:27
Q58, 4:12:40
Q59, 4:14:28
Q60, 4:19:48
Q61, 4:25:39
Q62, 4:28:52
Q63, 4:29:32
Q64, 4:32:55
Q65, 4:35:29
Q66, 4:50:04
Q67, 4:55:42
Q68, 4:58:36
Q69, 5:02:56
Q70, 5:10:32
Q71, 5:13:24
Q72, 5:21:08
Q73, 5:28:08
Q74, 5:34:14
Q75, 5:43:16
Q76, 5:51:17
Q77, 5:52:58
Q78, 6:00:28
Q79, 6:08:10
Q80, 6:13:28
Q81, 6:37:48
Q82, 6:45:45
Q83, 6:49:24
Q84, 6:54:00
Q85, 6:57:25
Q86, 7:03:50
Q87, 7:07:33
Q88, 7:11:11
Q89, 7:17:27
Q90, 7:21:37
Q91, 7:28:52
Q92, 7:37:47
Q93, 7:55:15
Q94, 8:07:00
Q95, 8:10:24
Q96, 8:21:05
Q97, 8:22:55
Q98, 8:26:30
Q99, 8:29:59
Q100, 8:33:33
Q101, 8:38:32
Thank you!! You’re awesome!
Thank you sir I love you
@@blackpenredpenHey bprp.if may ask, has there been any calculus question that you've personally created that had proved quite challenging for you to solve, ever before.
FUIYOH!
wow, thanks nathaniel barnett! I used these timestamps at LEAST ten times.
This might be the mathematics equivalent of David Goggins doing 4030 pull-ups in 17 hours.
except that nearly every college student taking a calculus course does this while studying at some point..
@@ryanspivey1819 Bro its impressive because he was doing it for 9 hours straight. By your logic, David Goggins doing 4030 pull-ups in 17 hours is not impressive either because there are teenagers who have done over 5000 pull-ups in their lifetime.
@@dokeo3333 That's not what I am saying. I'm saying all students have done integrals for 9 hours straight at some point.
@@ryanspivey1819 not all people do push-ups and not all people go to gym and not all people take calculus in college. both are impressive af.
@@ryanspivey1819 call anecdotal fallacy but I just never did or saw that in my life ever
Most impressive is that the kept holding the mic for 9 hours instead of putting it on his collar
😂
It is because mathematicians feel weird to leave a hand empty 😅
@@theunknown-qb9cjwhy?
@@matheusnunes970 because that'll turn the surface of his hand to an indefinite integral
😂😂😂😂😂😂😂@@axz0nice
Q1, 0:00:46 (u-sub)
Q2, 0:03:03 (trig identities + u-sub)
Q3, 0:08:23 (trig sub)
Q4, 0:12:34 (u-sub + IBP)
Q5, 0:17:02 (u-sub + trig sub)
Q6, 0:19:42 (u-sub)
Q7, 0:30:07 (u-sub)
Q8, 0:33:45 (linearity of integration)
Q9, 0:37:58 (trig identities)
Q10, 0:45:16 (partial fractions)
Q11, 0:48:30 (polynomial special products + u-sub + formula)
Q12, 0:53:16 (trig identities)
Q13, 0:59:06 (expansion)
Q14, 0:58:34 (u-sub)
Q15, 1:00:41 (u-sub)
Q16, 1:04:56 (trig identities + u-sub)
Q17, 1:07:27 (trig sub)
Q18, 1:12:27 (trig identities + u-sub)
Q19, 1:14:42 (trig sub)
Q20, 1:18:50 (u-sub)
Q21, 1:22:30 (proof of a reduction formula + IBP)
Q22, 1:25:14 (proof of a reduction formula + IBP)
Q23, 1:27:40 (proof of a reduction formula + IBP)
Q24, 1:37:44 (proof of a reduction formula + IBP + u-sub)
Q25, 1:42:58 (proof of a reduction formula + IBP)
Q26, 1:52:14 (box method)
Q27, 1:54:45 (u-sub)
Q28, 1:57:45 (algebra manoeuvres)
Q29, 2:01:49 (u-sub)
Q30, 2:04:49 (trig identities)
Q31, 2:24:38 (trig identities + Weierstrass substitution + partial fractions)
Q32, 2:27:17 (trig identities + Weierstrass substitution + formula)
Q33, 2:31:25 (trig identities + Weierstrass substitution)
Q34, 2:35:00 (Weierstrass substitution)
Q35, 2:37:20 (trig identities + Weierstrass substitution)
Q36, 2:42:02 (multiplication by the conjugate)
Q37, 2:44:24 (trig substitution)
Q38, 2:50:18 (algebra manoeuvres)
Q39, 2:51:53 (relation between e^x, f(x) and f'(x))
Q40, 2:56:12 (IBP)
Q41, 3:00:21 (u-sub + trigonometric integral)
Q42, 3:04:07 (trig identities + trigonometric integral)
Q43, 3:06:45 (trig sub + elliptic integral of the first kind)
Q44, 3:11:58 (u-sub + error function)
Q45, 3:19:02 (IBP)
Q46, 3:24:19 (IBP + Fresnel integral)
Q47, 3:28:36 (trig identities + trigonometric integral)
Q48, 3:31:54 (IBP + trigonometric integral)
Q49, 3:33:44 (u-sub + IBP + exponential integral)
Q50, 3:43:40 (u-sub + IBP + trigonometric integral)
Q51, 3:49:16 (trig identities + u-sub + elliptic integral of the second kind)
Q52, 3:55:44 (u-sub + IBP + Fresnel integral)
Q53, 3:59:50 (exponential integral + IBP + imaginary error function)
Q54, 4:03:18 (IBP + offset (or Eulerian) logarithmic integral)
Q55, 4:08:21 (exponential integral)
Q56, 4:09:21 (u-sub + exponential integral)
Q57, 4:10:27 (IBP + logarithmic integral)
Q58, 4:12:40 (trigonometric integral + IBP)
Q59, 4:14:28 (Fresnel integral + IBP)
Q60, 4:19:48 (Lambert W function + u-sub + IBP)
Q61, 4:25:39 (improper integral)
Q62, 4:28:52 (improper integral)
Q63, 4:29:32 (improper integral)
Q64, 4:32:55 (improper integral)
Q65, 4:35:29 (Gaussian integral + double integrals + Jacobian)
Q66, 4:50:04 (improper integral)
Q67, 4:55:42 (improper integral)
Q68, 4:58:36 (improper integral)
Q69, 5:02:56 (improper integral)
Q70, 5:10:32 (improper integral + partial fractions)
Q71, 5:13:24 (improper integral + u-sub + power series)
Q72, 5:21:08 (improper integral + Feynman's technique)
Q73, 5:28:08 (improper integral + u-sub)
Q74, 5:34:14 (improper integral + u-sub)
Q75, 5:43:16 (improper integral + u-sub)
Q76, 5:51:17 (odd improper integral)
Q77, 5:52:58 (improper integral)
Q78, 6:00:28 (Dirichlet integral + Laplace transform)
Q79, 6:08:10 (a variant of Dirichlet integral + IBP)
Q80, 6:13:28 (another variant of Dirichlet integral + Feynman's technique)
Q81, 6:37:48 (double integral)
Q82, 6:45:45 (double integral)
Q83, 6:49:24 (double integral)
Q84, 6:54:00 (double integral)
Q85, 6:57:25 (double integral)
Q86, 7:03:50 (double integral)
Q87, 7:07:33 (double integral)
Q88, 7:11:11 (double integral)
Q89, 7:17:27 (double integral)
Q90, 7:21:37 (double integral)
Q91, 7:28:52 (double integral over a given region)
Q92, 7:37:47 (double integral over a given region)
Q93, 7:55:15 (double integral over a given region)
Q94, 8:07:00 (double integral over a given region)
Q95, 8:10:24 (double integral over a given region)
Q96, 8:21:05 (double integral over a given region)
Q97, 8:22:55 (double integral over a given region)
Q98, 8:26:30 (double integral over a given region)
Q99, 8:29:59 (double integral over a given region)
Q100, 8:33:33 (double integral over a given region)
Q101, 8:38:32 (infinitely nested square root integral + power series)
thaNK HIM blackpen red pen
Your contribution is soooo helpful as somebody can review some important integral some times later! Thanks!
Thank you!!!
It would have taken you atleast 1 hr to type 😂
You will blow for sure 🌚
Somebody give this man a medal. Though I think I'm equally amazed that you carried that mic for 9 hours straight.
It is very refreshing to see the presenter to do things live, in real-time, with small typos corrected and elements of improvisation : that is exactly how these topics must be taught to any student body, not via a power point presentation :)
honestly, ppt math professors are the bane of my existence as a math undergrad
@@cameroncurtis7261it’s because they’re getting rid of blackboards. And if they still have blackboards they clean them with some chemical that makes it harder to see the chalk.
I have absolutely 0 idea whats going on in the video, but its still impressive!
Merry Christmas everyone!
Hi
Mery Christmas!!!!
U2
Merry Christmas calculus master! Love you 🎄😇
Merry Christmas! 2 million subs party next year!
Can we all stand up together for a moment and appreciate how much hard work and effort bprp is putting into the hard and intricate mathematical theorems to make them easier?
Cheers Steve, you're making my approach to calculus and maths for university exams easier! :)
Thank you!
The dedication this man has inspires me to very greater extent
I skipped ahead to see how badly your cheerful demeanour would be eroded after 9 hours of integrals, but you seem to be in great spirits throughout! Amazing! Also, you helped me remember how to do chain rule integration which I haven’t had to do in years, so thanks!
100 integrals part 3 please!!!!
😆
We’re driving a man crazy
Agree
💀
100 integrals for the new year
must say he is one of the best mathematics teacher i have ever seen [ he gives better pov to understand the question and solve it ] ...love from india 🇮🇳
Could anyone please do the timestamps for this (in the format of "Q1, time")
Thank you very much!
sure!!!
no.
@@yashashwisinghaniathat’s crazy bro
Im willing to do that tomorrow haha, been here for 8 hours and I need sleep, its already 1am
done, hope you and your girlfriend enjoyed your christmas!
oh wow.. i havent even come close to learning calculus in my school and yet i still enjoy and somehow understand these videos. congrats man
لقد ظننت انني الوحيد الذي لم يستجمع الرياضيات كما يجب 😢
@@a.Ak1non t’inquiète, moi aussi :)
calculus problems involve a lot of logic you learn in previous courses, in calculus you learn many laws and methods to solve specific problems and once you apply a rule that you learned, the rest is factoring and solving and stuff
@@pitchoutoum4840 (≥∀≤)/
You understand it slightly because you are just getting the style of it. Not knowing the logic behind will not help. But even understanding a bit without knowledge is good. I can see a good calculus student in you
You dropped this 👑
This guy is just insane
The efforts and dedication this guy has is really priceless
Q1 0:46
Q2 3:15
Q3 8:24
Q4 12:35
Q5 17:04
Q6 19:45
Q7 30:08
Q8 33:42
Q9 38:00 3answers with H.W
Q10 45:11
Q11 48:24
Q12 53:11
Q13 59:05
Q14 58:32
Q15 1:00:40
Timestamps (Powered by Merlin AI)
00:02 - Integration techniques covered in part 2
03:00 - Derivation of triple angle identity for sine
10:26 - Integration techniques and special integrals explained
14:02 - Integration by parts involves differentiating and integrating functions in a specific way.
20:47 - Using different substitution methods for integration.
24:37 - Integrating a complex square root fraction using a substitution method.
31:45 - Pairing up sine and cosine for integrals
35:07 - The integral of sine X plus cosine X is x minus Ln absolute value of sine X plus cosine X
41:54 - Integration of secant times tangent, and using trigonometric identities for simplification
45:37 - Integrating 1 over 7 - 6x - x^2 using partial fractions
52:38 - Using power reduction formula for sine squared
56:11 - Integrating trigonometric functions and exponential functions
1:03:46 - Techniques of integration involving substitution and trigonometric identities.
1:07:58 - Integrating 100 differentials with trigonometric identities
1:15:53 - Integrating complex trigonometric functions and inverse trigonometric functions
1:19:21 - Integrating square root and 1 + square root of x
1:26:22 - Key integrals reduction formula explained
1:30:05 - Integral transformation using power reduction
1:37:32 - Deriving reduction formula for integrating tangent functions
1:41:44 - Explaining integration using reduction formula
1:49:38 - Discussing reduction formula for integrals of secant
1:53:28 - Integration by simplifying complex fractions
2:00:58 - Integration techniques and approaches focus over domain restrictions.
2:04:30 - Explaining the integral of cosecant 2x and its significance.
2:13:45 - Derivation of sine and cosine using half angle substitution
2:17:39 - Using trigonometric identities to simplify the integral
2:26:09 - Integrating complex trigonometric expressions using substitution
2:30:02 - Integration using trigonometric substitutions
2:39:38 - Integrating complex fractions with shortcuts and simplifications.
2:43:28 - Integrating complex expressions using trigonometric substitutions
2:51:55 - Finding the integral of e to the x times sine x plus cosine x
2:55:36 - Integration by parts technique for solving integrals
3:04:12 - Integrating inverse sine x over inverse cosine x
3:08:01 - Explanation of elliptic integral of the first kind
3:16:23 - Solving integral using error function and special functions
3:20:37 - Integration using logarithmic integral poly logarithm
3:28:46 - Integrating sine of (1 + e^x) using angle addition formula.
3:33:39 - Exploring integration techniques
3:43:13 - Integration of 1/inv sin X follows a similar pattern as previous problems.
3:47:49 - Integration using trigonometric identities
3:56:02 - Exploring the integral of square root of inverse sine X
4:00:44 - Integration of e^(x^2) and e^x/(1+e^x)
4:08:49 - Integrating special functions and using substitution to simplify
4:12:54 - Integration by parts used to integrate sine functions.
4:21:34 - Integration by parts with exponential functions
4:25:32 - Finding the value of p for the integral 1 / x^p
4:33:41 - Understanding the convergence and divergence of integrals.
4:37:40 - Introducing the concept of polar coordinates and change of variables in double integrals
4:44:57 - Understanding polar coordinates integration
4:49:01 - Explaining the Gaussian integral with polar coordinates
4:57:00 - Integral of e to the x from 0 to 1 is equal to the integral of e to the x from negative infinity to 0.
5:01:16 - Understanding negative integral values
5:09:50 - Understanding and solving improper integrals
5:14:18 - Using power series for integration
5:22:08 - Deriving and solving the integral for x to the power of t
5:26:01 - Using innovative substitution techniques for integrals
5:34:56 - Integration using substitution and limits
5:39:08 - The integrals are shown to have the same value through a series of manipulations.
5:47:50 - Simplifying the integral using factorization
5:51:48 - Integrating art functions which converge to zero
6:00:34 - Laplace transform explained with examples
6:04:22 - Using Laplace Transform to find an integral
6:12:13 - Explaining the integral of sin^3(x)/x^3 over 0 to Infinity
6:16:59 - Applying power reduction formula to simplify the integral.
6:26:03 - Derivation of I double Prime of T
6:30:47 - Deriving the integral of a specified function
6:34:03 - Graphing equations of a line
6:34:33 - Integration of sine X over X
6:35:36 - Utilizing substitution to solve integrals
6:36:07 - Integrating cosine of Y to the third power
6:37:10 - Integration involving tangent and secant functions
6:37:40 - Discussing integration method by changing variable to ln of Y plus 1
6:38:48 - Understanding the change of variable during integration.
6:39:22 - Integration using change of variable method
6:40:29 - Comparison between DY first and DX first for integration
6:41:01 - Integrals and region boundaries
6:42:04 - Calculation of Jacobian for integral transformation
6:42:36 - Understanding the integral transformation process
6:43:40 - Solving for X and Y in terms of U and V using Jacobian
6:44:11 - Integrating x squared plus y squared using absolute value and U substitution
6:45:15 - Understanding vertex coordinates and equations of lines
6:45:47 - Integration of U^2 * sin^2(V) over specified limits
6:46:59 - Integration over a quarter circle region
6:47:30 - Double integral of square root of 1 + y^2 over a triangle region
6:48:32 - Integrating infinite series pattern
6:49:02 - Simplifying the integral using series and summation
Avg Asian at weekend.
Fr
You are a very good human being for giving free education. 🙏🏼.
Love and respect from India 🇮🇳
In my country the education is absolutely free, but I cannot say that all teachers here are good humans))
This is awesome, congratulations 😁
Thanks
Teachnology is amazing, It can show the talents of talented and hardworking teachers like you
your way of explanation is so amazing!!, even though i didn't learn power series, i was able to understand the last question. your students are really lucky to have you as their teacher!
At 44:00 to get the 3rd ans divide by( cosx)² will get sec²(x)/(1+tanx)² and so on
Incredible, you are indeed the GOAT of all Math content creators. 👍
مثال الجد والعمل ، ماشاءالله ، بالتوفيق
Thank you bprp for putting so much effort into this. We truly appreciate all you have done!
Hello Mr. BPRP! I'm a 16 year old guy from Brazil and I love your videos, they helped me a lot to learn calculus. Thank you for making me love math!
the mad lad did it again. some of these integrals are something else! happy new year!!
😆 thanks!!
You are a great guy@@blackpenredpen
I really enjoy mathematics when I see the explanations so perfect that you do, thank you professor for teaching us and showing us your passion for this beautiful science!!!!
Q1 - 1:01
Q2 - 3:23
Q3 - 8:40
Q4 - 12:46
Q5 - 19:59
Q6 - 24:45
Q7 - 30:20
Q8 - 34:03
Q9 - 38:10
Q10 - 46:00
Q11 - 49:04
Q12 - 53:20
Q13 - 59:06
Q14 - 58:34
Q15 - 1:00:55
Q16 - 1:05:32
Q17 - 1:07:41
Q18 - 1:12:47
Q19 - 1:14:55
Q20 - 1:19:04
Q21 - 1:22:52
Q22 - 1:25:38
Q23 - 1:28:00
Q24 - 1:37:53
Q25 - 1:43:05
Q26 - 1:52:22
Q27 - 1:55:09
Q28 - 1:58:18
Q29 - 2:02:05
Q30 - 2:04:58
Q30B - 2:21:35
Q31 - 2:24:54
Q32 - 2:27:22
Q33 - 2:31:39
Q34 - 2:35:13
Q35 - 2:37:30
Q36 - 2:42:11
Q37 - 2:44:42
Q38 - 2:50:48
Q39 - 2:52:11
Q40 - 2:56:22
Q41 - 3:00:41
Q42 - 3:04:31
Q43 - 3:06:58
Q44 - 3:12:24
Q45 - 3:19:33
Q46 - 3:24:28
Q47 - 3:28:48
Q48 - 3:32:19
Q49 - 3:33:55
Q50 - 3:43:57
Q51 - 3:49:28
Q52 - 3:56:00
Q53 - 4:00:00
Q54 - 4:03:31
Q55 - 4:08:31
Q56 - 4:09:29
Q57 - 4:10:41
Q58 - 4:12:47
Q59 - 4:14:10
Q60 - 4:19:54
Q61 - 4:26:08
Q62 - 4:29:02
Q63 - 4:29:50
Q64 - 4:33:04
Q65 - 4:35:56
Q66 - 4:50:30
Q67 - 4:55:51
Q68 - 4:58:53
Q69 - 5:03:21
Q70 - 5:10:47
Q71 - 5:13:55
Q72 - 5:21:31
Q73 - 5:28:22
Q74 - 5:34:48
Q75 - 5:43:49
Q76 - 5:51:30
Q77A - 5:53:11
Q77B - 5:54:50
Q78 - 6:00:40
Q79 - 6:08:21
Q80 - 6:13:38
Q81 - 6:38:06
Q82 - 6:46:12
Q83 - 6:49:48
Q84 - 6:54:17
Q85 - 6:58:10
Q86 - 7:04:38
Q87 - 7:08:03
Q88 - 7:11:46
Q89 - 7:18:04
Q90 - 7:22:21
Q91 - 7:29:10
Q92 - 7:37:58
Q93 - 7:56:50
Q94 (pi/2) - 8:07:48
Q95 - 8:11:23
Q96 - 8:21:41
Q97 - 8:23:38
Q98 - 8:27:14
Q99 - 8:30:54
Q100 - 8:34:06
Q101 (Bonus!) - 8:39:24
Merry Christmas Everybody!
100 EC. DIFERENCIALES 👉🖐 th-cam.com/video/Ffje0YYsyr0/w-d-xo.html
the PURE DEDICATION that goes in to these is absolutely insane. amazing.
Man really stood 8 hours in a go. Round of applause 👏
Does he not even go to the loo?
He really stood so far
Meet salim ahmad sir pw physics wallah 19 hrs , 17 hrs live class non stop
@@H15836 where?
@@turkeyphanthe is an Indian phy teacher
SInce bprp asked for it!
Q1: 0:40
Q2: 3:05
Q3: 8:24
Q4: 12:32
Q5: 17:04
Q6: 19:40
Q7: 30:07
Q8: 33:44
Q9: 38:04
Q10: 45:19
Q11: 48:19
Q12: 53:14
Q13: 59:05 (yes he does 14 before 13)
Q14: 58:15
Q15: 1:00:40
Q16: 1:04:55
Q17: 1:07:30
Q18: 1:12:30
Q19: 1:14:45
Q20: 1:18:55
Q21: 1:22:30
Q22: 1:25:15
Q23: 1:27:45
Q24: 1:37:45
Q25: 1:43:00
Q26: 1:52:15
Q27: 1:54:55
Q28: 1:57:45
Q29: 2:01:50
Q30: 2:04:50
Q31: 2:24:43
Q32: 2:27:18
Q33: 2:31:32
Q34: 2:35:03
Q35: 2:37:18
Q36: 2:42:03
Q37: 2:44:23
Q38: 2:50:23
Q39: 2:51:28
Q40: 2:56:13
Q41: 3:00:23
Q42: 3:04:23
Q43: 3:06:48
Q44: 3:12:00
Q45: 3:19:00
Q46: 3:24:18
Q47: 3:28:38
Q48: 3:31:53
Q49: 3:33:43
Q50: 3:43:43
Q51: 3:49:08
Q52: 3:55:48
Q53: 3:59:59
Q54: 4:03:18
Q55: 4:08:23
Q56: 4:09:23
Q57: 4:10:38
Q58: 4:12:43
Q59: 4:14:08
Q60: 4:19:53
Q61: 4:25:38
Q62: 4:28:33
Q63: 4:29:43
Q64: 4:32:58
Q65: 4:35:30
Q66: 4:50:10
Q67: 4:55:45
Q68: 4:58:40
Q69: 5:02:55
Q70: 5:10:35
Q71: 5:13:25
Q72: 5:21:05
Q73: 5:28:15
Q74: 5:34:15
Q75: 5:43:15
Q76: 5:51:20
Q77: 5:54:40
Q78: 6:00:30
Q79: 6:08:10
Q80: 6:13:30
Q81: 6:37:35
Q82: 6:45:40
Q83: 6:49:25
Q84: 6:54:00
Q85: 6:57:35
Q86: 7:03:35
Q87: 7:07:35
Q88: 7:11:15
Q89: 7:17:30
Q90: 7:21:41
Q91: 7:28:56
Q92: 7:37:46
Q93: 7:55:16
Q94: 8:06:56
Q95: 8:10:26
Q96: 8:21:06
Q97: 8:22:56
Q98: 8:26:31
Q99: 8:30:21
And finally, Q100: 8:33:36
?? Q101: 8:38:25
Thank you!!!
@@blackpenredpen no problem!! Glad to help 😁
He did not just do 100 integrals but he filmed from 6pm to 3am. That shows his hard work and dedication.
just found this channel and man as a 15 yr old entering his senior phase(where math gets real), I'm honestly excited after I've seen the dedication and expertise this man demonstrated. SO I hope ill be back in the next year or so actually understanding these concepts in sense.
All the best! Calculus is a fun experience, although frustrating at times. I hope you get to enjoy the subject as you go through this new phase of life
Wait in foreign countries( I am from India ) u guys study only calculus for a year ? My heart goes out to u
@@divinebanana8400 no not sure about that, i believe calculus comes in a later grade but not grade 10, calculus is near the end of high school for me (not so sure tho) but prolly more indepth in university.
Hi blackpenredpen, love the effort into these videos!
I recently realized I have a family member who is also a professor at UC Berkeley! He is in the physics department, Rene Bilodeau. Small world.
Happy new year from Canada.
Thank you!!! I am not a professor at UCB but am a graduate from there with a BA degree. 😃
The most patient man in the world
I really appreciate your hardworking, man!
hey BPRP, I just wanted to say how much I appreciate the content that you make and the incredible amount of work you put into it. you seriously have no idea just how much this content means to us and has helped us. I’ve been watching you since my first calculus class, and I have surpassed linear algebra largely thanks to the fundamental ideas that you have highlighted and reinforced in your content. thank you from the bottom of my heart.
if Q9 with the numerator and denominator dividing on cos²x, that would lead to dtanx/(1+tanx)² and a way for Q33 with multiplying 1-cosx up and down after decomposing the term sin2x in the denominator brings in (1-cosx)/sin³x as the integrand and results in c+[cscx(cscx-cotx)+ln|cscx-cotx|]/4 and Q35, c-2ln|cos(x/2)|; with the result of Q54, the x² term can be further operated; Q94, the result written down misleaded, π/2
we do not care
@@FantomaBatePalma01 a statement i don't care about either
Huge respect to this man who solve 100 integrals multiple times👍
you know the guy is serious when you see he has like 2000 marker pen in storage in a cabinet in the back
😂😂😂 I watched for 3 hours without noticing 2000 marker pens
BPRP has always been so passionate about math. He is my dream professor.
Hello ! I hope you see my comment
I saw this nice question so that I recommend it
The question is : solve the system of equations
a = exp (a) . cos (b)
b = exp (a) . sin (b)
It can be nicely solved by using Lambert W function after letting z = a + ib
Hope you the best ... your loyal fan from Syria
يستحق اكثر من مليون مشترك علي الجهد الي يبذل فيه 😭
اخيرا وجدت عربيا
@@omarelattaoui4988 hhhhhh morocco
Finally! Did every question in this!!, Really appreciate the efforts!
Awesome!! Thank you.
I found an interesting approach to Q49. I added an integral of 1/lnx dx and also subtract it to keep the original value. Then I used IBP on the integral -1/lnx and I got -x/lnx - the original integral, so they cancel nicely. Then i just solve the remaining integral as li(x), so I got my final answer: li(x) - x/lnx +C
Watching this without even knwing what the fuck hes talking about is so relaxing bro. Im just sittin here watching an asian guy doin math and its so chilling ❤
you're dedication is truly very inspiring, makes me want to be as dedicated as you while doing something
I said what I wanted to say, what a coincidence
This guy is just insane. Hats Off❤
What a man! Someone give this dude an award pls! So helpful!
Thanks for your amazing effort & great math content. Most meme-able moment: 5:42:30 “The PI just wants to show up.” x 3 🤩
An integral you should try: 1/ln(1/ln(x)) or -1/ln(ln(x)). It's quite a special integral. I also want to see how you are going to do it, since maybe the way I did it isn't the best. Btw. love your videos, keep it up!
I am watching this video for 9 hours as a review for an 1.5hr midterm exam tomorrow :) Learned many new techniques, which I wish I could recall tomorrow.
one day people will do bingewatch of his 100 Integrals videos as a challenge.
37:31 number 8 can be done with complex numbers as well it’s just long
My salute sir for your dedication for maths 🙏🏻
my guy was holding the mic for 8 hours straight with the same hand, thats even more impressive than the maths
thanks for the video ... great work and big energy
Some teachers are Doing this daily, Hats off to our only good teacher who love their profession
INTEGRAL AT 35:00 HAS CHANGED MY LIFE FOREVER
The Weierstraß subtitution is so elegant I love it!
A magnificent performance Sir. You are the greatest!
wow thanks i'm actually in the 7h and i so tired but it really fun doing it nonstop with you i swear, it really unfortunate that i didn't discover you before you really an inspiration and it was really fun doing it in one take with you, i'm looking to become better than you so don't give up on your perfect work and inspire people. thanks god there is some amazing teacher like you.
3:28:28 I think it should be +sqrt(2pi)... instead of minus (small mistake)
I agree
marker switching and holding a mic for nearly 9 hours straight... this mans is passionate.
Goddamn hats off to you man. Nonstop for 8+ hours!
Thanks.
This is like my dream video
My highest achievement is i have solved 600 sums in a week
12:21 "I want to finish this hopefully 6 hours 30 minutes. maybe 7" LOL
Yea I was a bit off lol
@@blackpenredpen 8 month old video and you respond in 30 mins 💯💯 keep up the grind, you make great content!
i didn't believe it at first so I dragged the track to speed up, and the first thing I saw was the clock turning smoothly. Respect. And thank you I needed this for calc 2
I literally have a calc exam coming up soon so this will be amazing practice material!!!
i dont know why this video is on my feed, but how he holds and switches both black and red pens is amazing! sooo fluid and smooth
This needs to be a sport.
This is a masterpiece.
“What terrible sin have I committed in my past life to deserve this pain? 1000s and 1000s of integrals!”
-BPRP
This is insanely awesome lmao it makes me want to go sit down and just practice along for as long as I can. This is such a great way to keep integration sharp.
Can't wait to see this once it is processed
This level of effective work and that too "continuously" ❤ is greaaattttt
Number 9)multiply nominator and denominator with sec^2x so we get integral of sec^2x/(tanx+1)^2 dx substitue u=tanx+1 Du=sec^2x so we get - 1/tanx+1 rewrite tanx as sinx/cosx, do the calculating and you end up with sinx/sinx+cosx +constant (sorry for my bad english)
Ahhhh yes!! Thank you!!
Would u mind telling me how to reach sinx/ sinx + cosx using this way? I tried manipulating -1/1+tanx but couldn't find how yo reach it, but you inspired me by multiplying by csc² which will end up in a nicer way
Maybe it is the R rule? And u are talking about Rsin(theta + alpha) or even the co-rule
4:08
41:00
1:03:00
1:19:30
1:24:00
1:29:40😀😀
1:38:36
1:52:40😀
1:55:34
2:16:00
3:04:50
3:20:50
3:27:19
3:30:20
3:42:30
5:12:28
5:46:00
6:10:20
6:21:00
6:42:42
6:47:03
why am I here? and Why am I watching it for last 7 hours?
The best teacher maths🎉❤
From Morocco 🇲🇦
This video inspired me to give up maths.
😭😭
My math teacher always said: Deriving is a craft, integrating is an art
Insane stuff.... subscribed
Thanks!
Q30, what about extending the fraction to sin(2x)/(1-cos²(2x)) and substituting u=cos(2x), then we get C-0.5*artanh(cos(2x)) quite quickly.
OMG! It was really challenging. But thanks for such a technical solution. This guy is really genius and intellectual. Enjoying the content of this channel.. Well done keep it up. #SUPERMATHS
One error I noticed - 4:39 --> sinx * (-2sin^2x) = -2sin^3x not -3sin^3x
Other than that great video! Keep up the great work you got me through all of Cal!
He corrects it at 5:38 👍
I wish you were my mathematics teacher❤!!
we need a part 3 with lots of integrals with logarithms and exponentials asap pleaseee
In 3rd part we are going to do comment , in order to bring part 4 and so on, keep y=x² on your faces🙂
Really enjoyed Q92. Well-done my man... Well done
I laugh out loudly when he said " yes I am serious we gonna do another 100 😂😂
Dude that's awesome! And crazy! Thank you for your upload!
This is just so incredible and amazing! Also, I would love to see like some sort of competition in this between maybe you and Dr. Peyam or something like that (Maybe something like the MIT Integration challenge thing, but I'm sure you guys would make it more fun), You guys could put a prize on it too! I'm sure it would drive a lot of viewers and be much fun!
As someone with essentially no knowledge of math I've no idea how youtube shows me these videos and why I watch them every couple of months.
I have been watching your videos since many years. You have been doing insane Sir! 😍