How to Integrate Using U-Substitution (NancyPi)
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- เผยแพร่เมื่อ 30 มิ.ย. 2024
- MIT grad shows how to do integration using u-substitution (Calculus). To skip ahead: 1) for a BASIC example where your du gives you exactly the expression you need in order to substitute, skip to time 1:30. 2) For an example where you have to REARRANGE THE DU by multiplying or dividing because the du has a different number or sign than what you need, skip to time 8:21. 3) For one where you have to REARRANGE THE U by subtracting or adding because the du expression cannot give you the expression you need, skip to 17:15. 4) For u-substitution with TRIG (SIN/COS) and the power rule, skip to 22:35. Nancy formerly of MathBFF explains the steps.
Follow Nancy on Instagram: / nancypi
Twitter: / nancypi
For my video on the BASICS of INTEGRATION, jump to: • Basic Integration... H...
With all u-substitution integration problems:
The FIRST STEP is to pick your "u". The best choice is usually the longer x-expression that is inside a power or a square root or the denominator, etc (in an "inside function"). Set u equal to this x-expression.
The SECOND STEP is to find "du" by taking the derivative of the u expression with respect to x. For instance, if you have u=3x+2, your du would then be du=3dx. **NOTE: Remember to include "dx" at the end of your du differential expression.
The THIRD STEP is to substitute u and du into the integral everywhere in place of x and dx. **NOTE: if your du does not perfectly match what you need in order to completely substitute before integrating, you must rearrange the du, or sometimes rearrange the u, in order to fully substitute before integrating. For an example of each, see example #2 (time: 8:21) and example #3 (time: 17:15).
The FOURTH STEP is to integrate, remembering to add "+ C" at the end since you integrated an indefinite integral (no limits). The du goes away when you integrate.
The LAST STEP is to "back-substitute" by replacing everywhere u appears with the x-expression that you chose u to be.
For more of my math videos, check out: nancypi.com
Does she have anywhere where we can donate to her for providing these wonderful videos? Made this so easy to understand and was way more helpful than my professor. Thanks so much for making such quality videos and going step-by-step. It makes those of us who are taking classes a decade after we finished high school much easier to understand! If you have anywhere I can donate to you for your time/help I would love to know!
Hi Melissa, yes here you go. I'm happy they've helped you! 💛 www.patreon.com/nancypi
couldn't have said it better my self
Sooo true.....wayyyyyyyy more helpful than my professor 😃
@@BST-vk7lb lmfao
u dirty dawg, we all know the real reason ur donating
can i substitute u for my professor
evil
What the heck r u....? I see u in every of her video. Youre learning, eh?
idk man
Nice one
What grade are you?
Cleaver af
The best thing about Nancy is that she never, never, goes into full math professor mode and says: "and it is obvious that...". She understands that if you are looking at these videos, there is nothing obvious about math. She does not skip three steps or assumes that you will figure it out. By far, one of the best teachers on this subject on line. Hope she will post more (she probably graduated already and is pulling mid 6 figures at some super corporation).
I also like that shes super sexy.
@@edwardthiccums2000 the main reason we come herw
@@edwardthiccums2000 that’s probably why she doesn’t post anymore.
YES this is why the teaching at Oxford is so bad !
A lot of math teachers/professors are dicks for some reason. I appreciate her approach.
Nancy, not only were you a great source of clear information and support during fairly trying times-the pandemic has pretty much wrecked our schooling system-but you're also a great source of inspiration and clear-headedness for all of thus. Thank you so much for you invaluable content.
I have retired form full-time work and want to be a math tutor, to work part-time. I took calculus over 20 years ago and I am relearning it. Nancy, your vids are crystal clear. You are slow and calm, and I love that. Great work! Thanks!
Would totally substitute U for my X.
john byrne corny
I couldnt resist, hope she gets a chuckle outta it
Bad joke
genius
Smart joke 😂
"Are the videos from the 2006 really helping???, yes TH-cam advertisment it is, now leave me alone jesus.
*jey sus* math does not change
jimi hendrix nice
Just try STUDY PUG!
had this exact thought!
swear to god if i get that ad again im gonna find the person who made it and shove my 'A' grade test paper in their mouth
I love your videos, they're always the MOST helpful out of every single channel on youtube. You're a great teacher thank you!
Out of all the tutorials I've watched? This is one of the most effective ways of teaching and as a student, it helped me the most to understand every detail about the topic that I am looking for. Hoping for the next problem tutorial. Thank you so much.
Took Calculus 1 two years ago and Pre-Calculus nine years before that. I'm in Calculus 2 now, and I had no idea there were such things as a "refresher course." Needless to say I've been trying to re-teach myself Trigonometry/Precalculus in order to relearn Calculus 1 in order to even grasp Calculus 2. My professor has been explicitly asked twice over the past few weeks, "How do you know what to take as u?" and his answer was the same each time: "Think of it as... an art. You can't really explain. It's uhhh, intuitive." (What an educator.) Sigh. These past 3 weeks have been rough. Like, really rough. Thank you for softening this hard life♥︎ You (and Professor Leonard) are incredible at translating this crazy conceptual language that is mathematics into sweet plain English. Thank you thank you thank youuu. My first exam is in a couple days and it's a sweet feeling knowing I might actually pass 😭
Did you pass
@@danny89620 Yes I did - actually aced the first exam this topic was in :)
@@itsabelleee how was calc2 ? is it as bad as they make it out to be? i’m approaching the final for calc1 this sem and i’m pretty nervous for calc2 from all the stories i’ve heard
I've studied calculus and I'm a teacher. These videos on calculus are easily the best series on the topic I've ever seen. Nancy relates easily to the real struggles of calculus students, each step in the approach connects clearly to the previous one, and her set-up of the clear board looks awesome but is very effective and non-distracting. Beautiful work.
@BallerJack05 nah she’s using mirrors
Or maybe ur a SIMP
@@Blalalala-xd5tl yeah,in the vid she s writing with her left hand,but in reality its ther right hand
WONDERFUL !! I just went through this entire video very, very slowly, making sure I understood absolutely everything that was written. And it was almost fun. I think this is as painless learning how to integrate using u-substitution will ever get. Thank you. Thank you. Thank you.
i have so much respect for this girl for being able to write everything in this entire video backwards just so we can see it the right way.
Are you being subtly humorous? I can't tell, but I wondered the same thing. I might be slightly stupid, but I'm pretty sure that's not a thing.
@@shlarry3184 i was joking halfway lol. I thought she rlly did that until i realized she probably wrote it normally but just flipped the video
@@SpitKid It's an interesting chirality proof brain exercise.
@@SpitKid Look at the dry erase marker. EXPO is the most common brand of dry erase marker. The marker has the word "EXPO" like backwards ("OPXE") written on it. So it does look like it was either left-right reversed or it was shot with a camera pointed at a mirror.
man u a special kind of stupid
I really like how you provide the different "types" of problems you will see when using this process. I know you do that with all of your videos, and it's really helpful for us to learn that, even if we are practically copying when we see it in application, but it makes it easy to catch on how it works in general later. In other words, the way you make your videos is probably the most helpful from what else I've seen on TH-cam. Thanks!
When she explains something complex, suddenly it becomes simple. Teachers around the world need to take this girl as an example.
Please keep up the amazing work! You got my support until the end!
Solid Chrome i
th-cam.com/video/y_XwQkchwrE/w-d-xo.html
Thing is that boys concentrate more so they understand easily.
@gunjanrana4474 as a girl I can confirm that I concentrate more than boys do 😏😏😏🏳️🌈
@gunjanrana and i am pretty sure I am not the only girl to concentrate more than boys....there must be many girls like me... Especially teenagers like me 😏😏😏😜
Nancy! Fewer tears have been shed after I discovered your videos. I'm beyond grateful.
Really impressed by your informative videos. You have made something that has been very difficult to understand in the past to something that is much easier to learn. I believe I have the ability but never had the right teacher to to break it down in such simple form. All students have different learning abilities. I think the problem is that some students are embarrassed to speak up. Keep up the good work!
Nancy, thank you so much for saving my sorry butt again. You got me through calc 2 three years ago, and now you're helping me review for Calc 3, Intro to Linear, and Statistics for ECE. Love your stuff - very clear, very concise, easy to understand. You might just be the only reason I get through this hellscape of a term.
Usually, I get distracted by the teacher if they look this good, but this channel has the opposite effect on me and helps me stay engaged and listening. I've come to enjoy topics I normally wouldn't have. Thank you so much!!
I love your teaching approach it's really great. You really introduce the concept nicely.
I feel like she is using hypnosis to make me focus on maths
😅😂 is that why I’m watching her videos even though I need the math for nothing? 🤔😂🤦🏾♀️🤷🏾♀️
th-cam.com/video/AU4XERCPjIs/w-d-xo.html
@@Jacob-ed6wv th-cam.com/video/AU4XERCPjIs/w-d-xo.html
So true 😂
A smart girlfriend is the best way to get through calculus. Or, it was in 1987.
Nancy - you explain everything so well. I wish that I had had a teacher as gifted as you when I was initially learning these concepts forty years ago. Thank you for all that you do. Please keep up your amazing work.
I’ve watched so many of your videos to help review and better my understanding for my Ap Calculus Final and your explanations and step by step examples have helped so much, i’ve better understood the concepts in the way you teach than any of my teachers in the past, thank you so much Nancy!!
One of the best teacher ever... Such a calm voice, calm way of teaching.. Great method of explaining things..
I'm extremely impressed with your ability to write everything in a mirror image perfectly
Bhamilton0347 . I like how clueless you are.
Silkie Shag It’s flipped along the x-axis. Rotation wouldn’t do..
@@zacriversjr7029 you are right , i made a mistake, but i think people understood what i tried to say. thanks for the correction.
@@silkieshag9703 😂 No Problem
You are innocent as a 🐰
Thanks to you and your old channel, I passed Calculus 2 so I don't really need to watch this video anymore. But I still wanted to give you the recognition, views, and likes that you deserve! Please keep the videos up. You are helping so many of us struggling students!
the detailed ques you give are what someone who took these courses many years ago needed for it to all come back, ty
Nancy, I am quite impressed with the way you teach this topic. Please, keep up the good work!
NancyPi is my girlfriend and she is just like the square root of negative 100: a perfect 10 and imaginary.
No other comment had been more math-ish.
@@parthmaheshwari3323 parth Gaming
@@ankitaaarya Yes?
Parth Gaming parth Gaming
Clean shot
That was seriously satisfying! A phrase i never thought I'd utter 🙂👍
WOW! Perfect presentation. I love the slow tempo. I've been out of school for 8 years and needed a refresher for going into Calc II. This was perfect. Thank you so much! LOL I thought I was good at writing upside down, but you are awesome at backwards. Very clever low tech approach. cool!!
She made this so much easier. I know my college professor has to get through all this in like 40 minutes and show multiple examples so I understand its hard for him to go through step by step like this. So to the people who take their time to go out of the way and post videos to help all of us who struggle, Thank you so much.l
Nancy you are awesome at teaching! Especially during this pandemic and with online school! I hope you have calc 2 videos so I can watch those next semester!
Nancy, you're such a wonderful teacher! You have really simplified the concept of u substitution for me! So much clearer now. Thank you so so much! Way better than my lecturer at university
you make reading & writing backwards look easy!
Nice to finally see codified WHEN to use them - Thanks.
I just refreshed my entire calc 1 class by watching these videos and I understand it way better. This channel literally is saving my college GPA
Honestly thought u-substitution was a difficult and I was quite intimidated by it but you explained it so well and I now have a better understanding of it🥺🥺thank you for this
it is easy just need practice to be perfect
Thank you so much for taking the time to make this video!!!!!
You are an excellent teacher, especially for people who are new or hardly know where they are going. Thank you!
I like how u make us feel like as a student you didn't understand certain steps and explain it well.... Love you♥️♥️
She had me at "You don't have to like math, but you can like my video"..!
Every math TH-cam out there is the nicest person i know
Thankyou Nancy Ma'am. It were you because of whom i was able to understand integration by parts as i was looking for this topic to master for physics. Thankyou once again Ms. Nancy!
Thank you so much for making this video,, i couldn't understand something since the last 2-3 days because I don't have a good basic foundation,,, it is so helpful to me ,,, completely cleared my doubts❤️
Blink twice if they're holding you hostage.
You noticed she seemed upset halfway through, too, huh? Lmao
Spray some pepper if they are causing you lust. - The Holy Fuck1ng Bible.
@ I am sure writing mirrored on a glass is not satisfying.
They are holding her hostage, on the other side they have a gun to her and the only way she can stay alive is by doing calculus.
@@ValAi178 she actually writes normal to her perspective, then they flip the video when editing. you can tell because her expo marker letters are mirrored
You're never allowed to go away, Nancy! I swear, I can struggle with a calculus concept for hours, but watch just one of your videos and suddenly everything is crystal clear! You make it so easy and I love your teaching style! Thank you!
You made a great impact in my studies, I started derivation and integration with your video and you made it so easy. I am very very thankful the most beautiful teacher.
I was like "Woah!"
Every single moment I watched this video.
I can't belive how simple it became when you taught it!
Thank you really!🙏🏻
I really liked the simplified patterns you taught to solve these questions.
"What happens when you have a trig function?" Well, I simply cry. However, this video was beneficial.
Hah, if you don’t like trig integrals you won’t like calc 2
@@fallout3freak360 You're right, I did not 😣
lol
Nancy, When you explain, it is clear as crystal. You are beautiful!
You deserve million of subscriber 🙂😊. it's really helped me to clear my concept when no other videos on youtube available like this . ❤️
Nancy pi thank you so much for your help and hard work and sweetness and just having a passion for helping people who are struggling with math 💛💛💛🌟🌟🌟 You saved my understanding for over a year now
were she my lecturer, I'll never skip a single class.
Get your grammar correct first you simp
shouldn't even be skipping classes smh
My lecturer spent an hour trying to teach this and just made me more confused. This is excellently taught and I now feel far more confident in using integration by substitution. Thank you so much.
Thank you Nancy for this. My daughter is having a hard time at school with this, I have learnt now, will teach her and ask her to refer your videos. Gratitude!
Your attitude/approach here is very smart and reassuring. Great calculus lesson and great professor.
Honestly GOD BLESS YOUR SOUL😭❤️❤️❤️
it took 8 minutes to understand 3 classes of Calculus 2. My professor needs to see this amazing educator!
Actually goated, love how you break down fancy concepts/rules into manageable steps
Thanks for this. You explain 50 pages of convoluted textbook gibberish in 25 mins. I'd fallen behind and really needed a refresher. Really grateful.
I’m paying $2k for my Calc 2 class. Attended 2 class of 4 hours and thought I would drop the class. Now I’m watching this video and I feel like I can tackle calc 2! Thank you, you’ve helped me since pre-calc
Why’d you pay 2k bro :(
2k??? where is that
@@or1343 university/colleege classes in the United states
2k is a steal compared to other college prices
No jokes from now on. IT’S STUDY TIME
Bhai kuch nahi idhar se mat padh ullu banari wo looks dikhahkar integration padhna hai to umacademy se padh
are bhai bhai
HAHAHAHHAHAHAHAHAHAHAHAHAHHAHAHAHAHAHAHAHAHHAHAHAHAHHHHAHAHAHAHAH
you are one of the best teachers that i can understant in the first example thank you so much
Wow this video has been so helpful. The way you explain step by step so calmly makes it easy to understand. Thank you so much for the video.
omg i have a quiz on this on monday thanks nancy!!
how did the quiz go?
i guess it went well but my teacher lost my quiz and gave me a 0
that sucks
Benjy Molina lol wtf
You are so cute tutor nancy!!❤️i really like your style and be a found of calculus🥰
5:45 that's where it just clicked for me! thank you!
I never thought I would fall in love with math and then NancyPi.....
it took me so long to figure out how you were writing backwards.. but now i realized you probably just inverted the video lol
You are intergreat
Oh for the love of God, *STOP!*
Karina De Leon corny
th-cam.com/video/y_XwQkchwrE/w-d-xo.html
@ god has no place here
ive never been so intrigued by the u-substitution way of of math! It is so compelling and her boo-manerisms are very great at explaining the topic.
Thank you so much you are such a talented teacher. It's so relaxed here and not intimidating. I love it
Genius Nancy said calculus is everyones favorite lol. Greatest teacher and a comedian!
I can’t imagine such beautiful lady can teach math in such beautiful and understandable way
Thank you for your great help
I introduced your channel to my daughter who is taking geometry. Thanks for making a page with really easy to follow teachings
Thank you Nancy! I just watched my professors zoom recordings on repeat to no avail. You made it click though. I have a test due by midnight on substitution. Wish me luck!
THANK YOU SO MUCH. I ONCE THOUGHT I WAS DUMB BUT U CAME TO RESCUE ME FROM THE DARKNESS OF FAILING MATH. I APPRECIATE YOUR EXISTENCE AND WORK!
why do people like her not have millions of subs, they're doing more good than rice gum and jake paul
if she dabs she will get famous
Think about the potential audience size. People who are using TH-cam specifically for Calc 2 versus people who are using TH-cam to consume "entertainment media", the market sizes of those two population groups are wildly different, and thus, the subscribe base is usually commensurate with that.
Not saying it's wrong or right, but that's why.
@@vincentgrimaldi3652 well it is since humans prefer entertainment over work and studying.
Please don't ever take these vid's away they are priceless
Thank you so much, needed a recap and you've explained it so thoroughly, the technique has clicked again!
Next Video Suggestion: Calc 3 - Scalar Multiples (Vectors) and Parallel Vectors
yes please!
Yes please
I see vectors in my sleep paralysis
Sounds like you can teach the whole material just via the comment thread
literally helped me more than my calc professor...
One of the best explanations on this topic I've ever seen.
thank you so much nancyyy
Love how she's laughing at 5:52 because she has covered the pink one from the wrong side.
Nancy you are super amazing. When someone is such an expert in Kenya will call him/her Fundi. Fundi Nancy! Thanks a lot!
So relaxing and slow paced. Perfect for my learning style
i like how you explain even the smallest changes. the best
I think the most impressive part is that she's doing this while writing backwards. I can bearly manage it forwards
U can write normally and flip the vid in editing
if you look reaaaaally closely, you can see that she is teaching math
Thank you, Nancy.
wayy more easy to understand than my teacher. This all finally makes sense now!!! I might actually pass this class now that I've found you, thank you!
I love you
So much
I was so lost (in calc)
And now I am found
Amazing grace
YES.......Nancy I am one step closer to winning a Nobel prize >:) Thank you
Xavier Rodriguez v
This video is very helpful for me. I am taking calculus now and it helps me learn this process.
Thanks for the step by step treatment of integration using U-Substitution which made me understand the subject quite comprehensively.
the integral of x\/x+2 was on my test and this helped me
Hek yeaaa this is what I exactly what I needed to refresh for my calc 2 .. NANCY YOU ARE AWESOME... THANX BUT IF IT'S NOT TO MUCH TO ASK CAN YOU PUT VIDEOS ON CYLINDRICAL SHELLS ROTAITNG ABOUT X AXIS
Stanley Miranda ikr she is😍🙏
I hated that so much. It's the reason I don't tutor calc 2.
That stuff along with the optimization and related rates made me regret taking calculus
Just Google Shell Method
Thank you
Hello, Nancy. I would like to say, thank you so very much for sharing us with the effect video additional easy to understand concerned all the examples with these calculation simples of their Substitution. You’re very helpful, very useful and understanding from what else I’ve ever seen on TH-cam to made very clear.
Such an Amazing teacher i had ever view .so polite and so grateful 💞
54 previously difficult integration sums disliked the video