For question b) make u = x + 1. Then x^2 = u^2 - 2u + 1. The expression then becomes (u^2 - 2u + 1)/u^4. You can split it up into three fractions, simplify, and then replace each u with x + 1. You'll get the exact same thing as he did in about 1/10 of the time.
They're the roots of the factorized polynomial that's under the fraction. They're good choices, because if you multiply through by x(x-8), and then plug in x = 0 or x = 8, the stuff that's multiplying the coefficients A and B will become zero, so you've effectively isolated the other one.
For (b), there is another way(more systematic) to determine A, B, C, D. After getting rid of denominators, you can keep differentiating both side and determine one coefficient at a time by substituting x with -1 This way you can find coefficient D, C, B, A in this order. Thanks for the video.
You can imagine it as taking the limit as x goes to -1 if it confuses you. The equality in the previous step has meaning everywhere, including in a neighborhood of x = -1, so you're allowed to take the limit as x goes to -1.
When I was 17 years old. People in class used to do these problems by the speed of lightening. I couldn't understand much then. Now I am able to grasp the theories after 15 years. I love 'em!!
For b) just do y= x+1 tven the fractional becomes (y-1)^2/y^4 i.e. (y^2-2y+1)/y^4=1/y^2-2/y^3+ 1/y^4. Now just do y=x+1 to get 1/(x+1)^2-2/(x+1)^3+1/(x+1)^4.
I'm your integral presentation fens and often watch your video also. Regarding to your question (b) I use a fresh smart concept that fully take away PF decomposition 4 general parts express. I just write down one question that involve all the constants, then simplify it and directly get the answer, it taken about 10 seconds. My way never being any calculus text books before. If you interested it, I'd like share with my this SC to you.
6 = T Topology Operator D = 6 Dimension 8. Obisiously Unique Topology R. Topology R Six Under Eight Writning Rule Position Depositive paint six flag equal eight. Topology Paint Law Degraphy.Option P Image Paint = Kash Flow Work = Unique P Chart.
@@kylesheng2365 One in which he actually explains what the hell he's doing? All I see is him hiding some things with his arms and pulling numbers out of thin air. I understand this video was meant for students who attended a particular lecture by a certain professor and hence are supposed to already be familiar with the technique, but here on UA-cam I'm sure that's not the case for most viewers.
@@agustinl2302 there is a good blackpenredpen that explains how the cover-up method actually works, don't bother watching these mit videos because they are reviews for students who are taking the course
Could somebody please explain the point at 7:37, where four different denominators are used, each with a different power. Why isn't (x + 1)^4 used for each term? I'd be grateful if anyone can explain this.
could someone please take a look at the following: x^2 -19x + 15 all over (x-1)(x-2)^2 = A/(x-1) + B/(x-2) + C/(x-2)^2 ... now it makes perfect sense to me that C/(x-2) is incorrect. However, (x-2)^2 = x^2 -4x + 4 and if you said A/(x-1) + (Bx+C)/(x^2 -4x + 4), you'd still end up getting the wrong answer. I don't see where the process becomes inconsistent. Thanks!!!
Bx + C is used when you have something like x2 - 3x + 2 (ie) when it's not possible to factorise it into repeating factors. On the other hand, C/(...)2 is used when (...) is a repeated factor in ur original question. Hope that helped Edit- I know it's 3 years too late but still
at around 14:04, he says we can sub in x = -1, but doesn't that mean we divided by 0 in the previous step when he divided everything by x+1 ? is that legal?
How do I do things with quadratics and Ax+B stuff? I'm super confused with my homework. Of course by the time anyone's replied to me, the homework will be due, but I still need it explained to me.
My only issue is you tend to run through certain areas where you assume people understand. he explained mostly everything well but it got a lil confusing at times.not bad tho...
separate it like : 2x/denominator + 2/denominator. The first part can be solved by substitution using 4x^2 + 1 = t. The later part has to be solved like 2/(4x^2 +1)^2 = Ax+B/(4x^2 +1) + Cx+D/(4x^2 +1)^2. Then substitute 4 random values you'll have 4 equations and 4 unknowns, solve by elimination.
Integration and differentiation are 2 of the most fundamental tools of modern maths . Without them Maths would still have been stuck in the 16 th century , so would have physics and modern technology wouldn't have been born . But what many people ask is when will I use calculus or trigonometry in real life . Well if one doesn't go in a science related field , one probably won't . But Maths and Science would give the person a deeper understanding of the world . Also whenever we learn difficult stuff our brains get healthier . What that means is that the connections between our neurons get thicker . One might make a smart , important life decision at the age of 40 just cuz he/she learn how to find the height of stuff from far away in class 10th.
You are not suppose to talk in in class. As a sum of fractions were each fraction is a part of the total number of fractional terms. Each fractional part is a partial fraction.
@Frycek216 ^.^ It's good to see that you are either trusting enough of some MIT guy or swell at math yourself. I got curious when I saw the opposition to the answer in the video. However these two 'college' kids may just be completely dreadful at math :D. But I do wonder how they got a negative rather than a positive?? Imma say iss da luck a da dumb lol
Time stamps for exercises:
Part a: 1:41
Part b: 7:07
Part c: 15:27
Part d: 16:36
Professor Joel Lewis thank you for a powerful demonstration of the techniques of integration in Calculus.
For question b) make u = x + 1. Then x^2 = u^2 - 2u + 1. The expression then becomes (u^2 - 2u + 1)/u^4. You can split it up into three fractions, simplify, and then replace each u with x + 1. You'll get the exact same thing as he did in about 1/10 of the time.
They're the roots of the factorized polynomial that's under the fraction. They're good choices, because if you multiply through by x(x-8), and then plug in x = 0 or x = 8, the stuff that's multiplying the coefficients A and B will become zero, so you've effectively isolated the other one.
I've been learning this in school, and it went over my head... And just 4 problems made me confident. Thanks!
For (b), there is another way(more systematic) to determine A, B, C, D.
After getting rid of denominators, you can keep differentiating both side and determine one coefficient at a time by substituting x with -1
This way you can find coefficient D, C, B, A in this order.
Thanks for the video.
thanks for sharing . wonmu hur
Didn't know David Archuleta became a MIT professor after being a singer for a long time. All jokes aside, this lecture was very interesting.
I like this video. It's clear, it's well-explained, the chap is good-natured. It's given me some good ideas for teaching this subject.
Brilliant teacher. Thank you very much.
I apologize. Watched this again and all became clear! Many thanks,
I am from India 🇮🇳
Your teaching best
You can imagine it as taking the limit as x goes to -1 if it confuses you. The equality in the previous step has meaning everywhere, including in a neighborhood of x = -1, so you're allowed to take the limit as x goes to -1.
Would be great if you start from the beginning of all steps and complete all steps
I agree … horrible teacher
i think u shld do everything step by step .. cheers...
When I was 17 years old. People in class used to do these problems by the speed of lightening.
I couldn't understand much then. Now I am able to grasp the theories after 15 years.
I love 'em!!
Really good extensive summary of partial fractions.
really usefull to refresh PFD for my computational methods class. thanks!
For b) just do y= x+1 tven the fractional becomes (y-1)^2/y^4 i.e.
(y^2-2y+1)/y^4=1/y^2-2/y^3+
1/y^4. Now just do y=x+1 to get
1/(x+1)^2-2/(x+1)^3+1/(x+1)^4.
I'm your integral presentation fens and often watch your video also. Regarding to your question (b) I use a fresh smart concept that fully take away PF decomposition 4 general parts express. I just write down one question that involve all the constants, then simplify it and directly get the answer, it taken about 10 seconds. My way never being any calculus text books before. If you interested it, I'd like share with my this SC to you.
For letter a it should be x^2-8x+8x+4/x^2-8x then split to x^2-8x/x^2-8x minus 8x+4/x^2-8x then simplified to 1 +(8x +4)/x (x+8)
You are referring to another lecture .imlooked at MIt index. Feeling overwhelmed
6 = T Topology Operator D = 6
Dimension 8.
Obisiously Unique Topology R.
Topology R Six Under Eight Writning Rule Position Depositive paint six flag equal eight. Topology Paint Law Degraphy.Option P Image Paint = Kash Flow Work = Unique P Chart.
The variable coaficiant value would change during each modified factor creating an equivalent numeral .
the cover up method is great !!!!!
Thank you,your passionate teacher!
i like this video so much, it learn me alot how to solve partial fraction problems. thanks alot
Such a short video and still so helpful
Thank you
13:17 why not B=1 immediately because left side only have x^2 and right side only have Bx^2 ?? then plugin x=0 and finally get C=-2
there is a short cut for (b): let u=x+1. that becomes (u-1)²/u^4 = (u²-2u+1)/u^4 = 1/u²-2/u^3+1/u^4 replace back the u by x+1. piece of cake.
the only problem in this video when he hides the Numerator and denominator this technique little bit confusing he could do it in better way
What is the better way?
@@kylesheng2365 One in which he actually explains what the hell he's doing? All I see is him hiding some things with his arms and pulling numbers out of thin air. I understand this video was meant for students who attended a particular lecture by a certain professor and hence are supposed to already be familiar with the technique, but here on UA-cam I'm sure that's not the case for most viewers.
@@agustinl2302 there is a good blackpenredpen that explains how the cover-up method actually works, don't bother watching these mit videos because they are reviews for students who are taking the course
@@agustinl2302 this is the video ua-cam.com/video/fgPviiv_oZs/v-deo.html
Clear as mud.
I finally know what Jordan Schlansky does.
dont leave
the page...
need more
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to write
information by
great teacher
online I'll
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Peace
Nice
woow i like this video u really got talent keep it up
It's fucking MIT obviously it has talent.
good working,
term: Decompose
Nice examples
For those of you who have trouble understanding the cover up method, here is a more detailed explanation:
ua-cam.com/video/f-2YYFEmJJo/v-deo.html
Amazing. Thank you so much!
Could somebody please explain the point at 7:37, where four different denominators are used, each with a different power. Why isn't (x + 1)^4 used for each term? I'd be grateful if anyone can explain this.
I Really Like The Video Partial Fractions Decomposition From Your
could someone please take a look at the following:
x^2 -19x + 15 all over (x-1)(x-2)^2 = A/(x-1) + B/(x-2) + C/(x-2)^2 ... now it makes perfect sense to me that C/(x-2) is incorrect. However, (x-2)^2 = x^2 -4x + 4 and if you said A/(x-1) + (Bx+C)/(x^2 -4x + 4), you'd still end up getting the wrong answer. I don't see where the process becomes inconsistent.
Thanks!!!
Bx + C is used when you have something like x2 - 3x + 2 (ie) when it's not possible to factorise it into repeating factors. On the other hand, C/(...)2 is used when (...) is a repeated factor in ur original question. Hope that helped
Edit- I know it's 3 years too late but still
Very entertaining.
Ok long story short
These are the kind of problems Indian highschool students solve. You guys are solving these in uni?
How come D =1 in the second example?
Thanks for sharing
in the 1st example where do you get 0 and 8? the numbers you plugged in for A and B. I dont understand that part.
Could somebody please explain why the degree of the numerator must be lower than the degree of the denominator?
lol its so funny how you walked out of and then came a back a few seconds later
like as if you had been gone for awhile
For those of you saying that he's a bad prof, you clearly lack the fundamental techniques of solving integrals.
at around 14:04, he says we can sub in x = -1, but doesn't that mean we divided by 0 in the previous step when he divided everything by x+1 ? is that legal?
How do I do things with quadratics and Ax+B stuff? I'm super confused with my homework. Of course by the time anyone's replied to me, the homework will be due, but I still need it explained to me.
LMFAO it's been two years and no replied😂😂😂😂
🤣😂is it still due??
My only issue is you tend to run through certain areas where you assume people understand. he explained mostly everything well but it got a lil confusing at times.not bad tho...
Super!!!
it's possible to be gone for a while if the video is cut x-x
Why (c) is done? How can we integrate it?
separate it like : 2x/denominator + 2/denominator. The first part can be solved by substitution using 4x^2 + 1 = t. The later part has to be solved like 2/(4x^2 +1)^2 = Ax+B/(4x^2 +1) + Cx+D/(4x^2 +1)^2. Then substitute 4 random values you'll have 4 equations and 4 unknowns, solve by elimination.
@@mayurkulkarni755 good explanation. thanks
@CPPA LOL. You're right. Why would someone do that?
if luis rossmmann drop out why he is teaching in mit?
How did you get 36
Explained very well😂
Wooo I like this vedio
I understand nothing here and I'm 30 but it looks fun just wish I could have someone to hold my hand and walk me through it. Too bad I'm dim
I like This Video :)
integration of 1/x(x+2) any one help please
Hi I am from Turkey 🇹🇷🇹🇷
Unique gait.
Where it is useful in life...?...I am a teacher educator of mathematics..I need answer during teachers traing...can anybody help me?
Integration and differentiation are 2 of the most fundamental tools of modern maths . Without them Maths would still have been stuck in the 16 th century , so would have physics and modern technology wouldn't have been born .
But what many people ask is when will I use calculus or trigonometry in real life . Well if one doesn't go in a science related field , one probably won't . But Maths and Science would give the person a deeper understanding of the world . Also whenever we learn difficult stuff our brains get healthier . What that means is that the connections between our neurons get thicker . One might make a smart , important life decision at the age of 40 just cuz he/she learn how to find the height of stuff from far away in class 10th.
NOP!
You are not suppose to talk in in class. As a sum of fractions were each fraction is a part of the total number of fractional terms. Each fractional part is a partial fraction.
Well there is a quicker way, but okay. Nice video.
@Frycek216 ^.^ It's good to see that you are either trusting enough of some MIT guy or swell at math yourself. I got curious when I saw the opposition to the answer in the video. However these two 'college' kids may just be completely dreadful at math :D. But I do wonder how they got a negative rather than a positive?? Imma say iss da luck a da dumb lol
MIT行きたくなる笑
Sorry I don't understand. This is not for me!
are the previous 6 message posts from the same person?? Lol each given on the same day and every word is capitalized. hmmmmm :p
#POW
Joel is kinda cute
i really dont understand him :(
@alternateatheist You're both completely awful at math... ^^
cover up explanation is confusing
Sorry, but you turned something incredibly simple into an absolutely confusing piece of blah blah.
Too long steps
in the 1st example where do you get 0 and 8? the numbers you plugged in for A and B. I dont understand that part.