# Basic Integration… How? (NancyPi)

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Published on August 22, 2018 by

For my video on how to integrate using U-SUBSTITUTION, jump to: https://youtu.be/8B31SAk1nD8
For my video on how to do INTEGRATION BY PARTS, jump to: https://youtu.be/KKg88oSUv0o

1) POWER RULE: If you're integrating a polynomial, or just a power of x, you can use the Power Rule on each x-term in the polynomial. The Power Rule says that for a term that's just a power of x, such as x^3, you can integrate by raising the power by 1 AND dividing by that number (the new number you got by increasing the power by 1). For example, the integral of x^3 would be (x^4)/4. If there was a constant multiplied in front of the x-power, you can keep the constant and integrate the rest of the term (Constant Multiple Rule). For example, the integral of 6x^2 would be 6 times (x^3)/3, which simplifies to 2x^3. You can repeat these steps to integrate every term in the polynomial and string them together for the full integral. You can also keep the addition and subtraction between the terms (because of the Sum and Difference Rules). NOTE: The anti-derivative of a constant (just a number) is always that number times x (the Constant Rule), so the integral of 1 is 1*x, or x. At the end, it's very important to remember to add a constant of integration, to include a "+ c" at the end of your answer, when it is an indefinite integral (integral with no limits). ANOTHER NOTE: The Power Rule only works when the power is not -1.

2) NEGATIVE & FRACTIONAL POWERS, and RADICALS: For negative powers, you can still use the Power Rule, as long as the power is not -1. For fractional powers, you can also use the Power Rule. When you increase a fractional power by 1, you will have to simplify the power (before integrating) by getting a common denominator. For roots, like the square root of x, it's best to rewrite the radical as a fractional power, and then use the Power Rule.

3) IF THE X POWER IS -1 in the integrand, either written as x^(-1) or 1/x, you have to use a special rule, the LOG RULE, that you can find on a Table of Integrals. It says that the anti-derivative of x^(-1), or (1/x) is the natural log of the absolute value of x, plus c.

4) MORE ALGEBRA: Sometimes you may need to do a bit more algebra before integrating, so that the integrand is in a form that fits a basic integration rule, like the Power Rule. If you're integrating a rational expression, you can sometimes separate the numerator, or break the fraction into separate fractions, simplify each term, and then integrate with the Power Rule. If you have a product of x expressions, you can multiply it out, or distribute the factors so that you have just a polynomial (and can use the Power Rule).

5) TRIG & EXPONENTIAL: You can find a lot of trigonometric (and exponential) integral rules in the Table of Integrals. If you don't see it in the table, you may need to use a trig identity first, to rewrite the integrand into a form that you can integrate.

For more of my math videos, check out: http://nancypi.com

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• Thank you Nancy

• Oh Kid Muscle…

• Nice vid ma’am !

• So ja nind NAHI ari kya

• @abcd xx lol

• Only Nancy could make me watch a video on Integration after she already helped me pass Calculus.

• man I’m re-watching cuz I’m a math major in college and I got rusty after not doing this for so long lol

• @Parmesan can uhelp pls

• @Strange Person CORRECT I AGREE

• For Simple solution visit

Classic Mathematics

• Hi

• OMG Nancy, how did you do that? Just a wink and the board cleared for you, just like Samantha Stevens on Bewitched!! LOL

• Holy Hotness Batman…..Where is the “Add To Cart” Button ?

• Hi Nancy, I absolutely love your videos! Can you make a video on conics, like hyperbolas, parabolas and such? Thank you soooo much.

• It’s 1:30 am in India and I’m differentiating

• computational integration is where it at

• Thank you, Nancy! Please make more calculus videos. You explain the best!

• 😁

• 😊

• Is it possible for you to make a video on related rates? Thank you

• Calculus rainbows

• Perfect timing! I have a quiz on integration tomorrow for Calculus II! Thanks Nancy! You and Professor Leonard have singlehandedly saved my butt when it comes to math

• can I integrate you into my life

• @Xαԋιԃ ƙԋαɳ ┐( ˘ ､ ˘ )┌

• (1/2)*you^2

• If that is you on the picture, I also want to integrate you in my life ×) what kind of cosplay is that if it’s even cosplay. It’s probably not and I am stupid for asking lol

• Integration by M. Rafi
Easy way to understand integration

• integrate your ASS first, it will vanish like a fart in the air.

• A review before I start Calculus 2 thanks Nancy

• can you do a video finding the area under the curve next (like using right and left endpoints of rectangles)

• Yay, it worked! I asked for it and here it is! Thanks 😁

• I remember when this was sooo confusing. Your videos are great at refreshing my memory and reigniting my admiration for math.
Thanks Nancy 🙂👍

• Have I mentioned how delightful you are? If I did, disregard this, it still holds.

• Could you post more integration rulers that i didn’t-have in high school please !!😭😇

• aLidjaoJgf Hi kids

• Very nice

• Ive already graduated in aerospace eng and im still watching this. I dont know why…guess its good to keep brain awake

• Nice one Patrick, ze is indd wel heel erg knap

• I suspect you’re being asked to find the maxima/minima of a quadratic. For example if a rocket is launched in the air with height given by h(t) = -16t^2 + 128t + 10 (h in meters, t in seconds). You can want the vertex. The t coordinate (often you have x instead of t) is given by t = -b/(2a) = -128/(2*-16) = 4. The rocket reaches its maximum height after 4 seconds. To find out what that height is, plug t = 4 into the function. h(4) = -16(4)^2 + 128(4) + 10 = 266 meters.

• Nancy….If you make a video on trigonometric integration….I promise to win a noble prize in physics to benefit all of humanity

• Xavier Rodriguez master the identities its your best bet

• actually she already did it but she didn’t upload it yet on her new channel ( i’ve already watched her old vids like this one but now they’re gone :/ )

• Thank you soooooooo muchh mam………

• Is there any way for finding the constant or it is impossible to find..?

• It depends on the use of the integral. When integrating data from a sensor, the constant is set by a “reset” when the system is in a known state. For example, a computer mouse works by using a laser to sense its velocity relative to the surface it’s on. The computer integrates the readings to move the pointer on the screen. Because of drift due to inaccuracies, the pointer often gets out of sync with the actual position of the mouse, at which point one fix is to “reset” the integral by moving the mouse into a corner.

• If you’re given a pair of numbers to plug in to the integrated function, yes. That’s called an initial condition.

No idea what that other guy is talking about.

• The derivative of a constant is always zero. So yes, it is impossible to find the constant.

• As NiHaoMike says, it depends on what you are doing. Integrating between limits, C will subtract from C and thus disappear. Another practical case is integrating the bending moment equation for a beam, integrating the first time (actually the third integral) will give the slope at any point on the beam and it is necessary to evaluate C, integrating again (fourth integral) for deflection at any point, a new C appears and it is possible to solve for that too. It’s been almost 40 years since I did this stuff and I can’t recall how to solve for C in each case. I think it may be setting X at a point where it is known that the slope is zero and similarly for the deflection. So any term containing X will go to zero but C will remain, not sure, memory failure.

• Great video, I might be wrong but I think before this video you only taught pre-calculus math. I hope you get into even more advanced stuff.

• Am I the first to make an “integral of e to the xy” reference here? 🙂

• I like math, ugh do you have a boyfriend? I wqnt to learn more math now.

• Hi Nancy can u plzz make a video on integration by partial fraction and integration by ILATE rule plzz i m having my exams next month and I dont know a bit bout these

• Hi Nancy!

I’ve watched a heap of your videos over the past 3/4 years. I just wanted to write a comment to say thanks. I’ll be starting my first job as an engineer in a few weeks.

🙂

• Nice! i have just started my 4 year course to train as a B1.1 license engineer, any tips?

• @The Sovereign Onion get swole

• With nancy and prof leonard anybody can be ace calculus 1, 2 and 3

• sinx/(1-cosx^2) can be solved with power rule, I had a nagging doubt that I could do it like that so I had to get out of bed at 2 am to try it, because math is awesome

• “Its okay, you dont have to like maths, but you can like my video.”
She’s funny 😂😂😂

• @Ishan Nair other dude

• @Arnav Upadhyay arnav you a simp 😂😂😂

• @Catalyzt you seem like one

• ssiiiiiiimp

• Thanks for the vid, Nancy! I was so sad when MathBFF stopped making videos, but I’m so happy to see that you’re making calc videos again. I loved some of those old videos about advanced integration techniques that have sadly been taken down. Do you think you’ll be redoing those any time in the near future?

• Is this calculus 1?

• Maths has become easy after learning from miss Nancy

• Please can anyone explain to me how at 7:00 x^-2/-2 simplified to -1/x^2?
Thank you!

• (x^-2)/(-2) = (1/x^2)/(-2) = (1/x^2)*(1/-2) = (-1)/2x^2

• A lot of students give up because no one tells them or convinces then why they need calculus
+nancypi
Maybe can do a video about that ?

• Because in order to earn a degree you need to be able to do upper-level math

• Calculus is found in alot of palaces. It is found in physics(when studyig about gravity, thermodynamics, quantum physics), it appears in business(when studying about prices and other models), it appears in geometry, computer science, biology everywhere

• Depending on what role you do will depend on whether you actually use calculus. For example, if you are a web designer you won’t even touch calculus but if you are working in AI/machine learning you will utilise alot of calculus/linear algebra/statistics

• thankx for coming back!!! your videos are really helpful and i have been watching your videos fora while

• Your videos are longer!! These are wonderful, from the bottom of my heart, thank you. Please more CALC 2 ……

• Thank you very much

• ok

• You are awesome!!!!Lots of love from Bangladesh!!!!!

• Veryy clear simple, you’re soo perfect😊

• *Thanks Nancy!*

*I’ve bookmarked some of your videos back then and suddenly the videos got removed from your previous channel (mathbff). I just wanted to write to say thank you for re-uploading the videos.*

*It really helps a lot* 🙂

• Thanks, this is a great refresher as I get started in Physics. Nice video: good speed, good diction, well explained.

• How are you writing in the opposite direction

• Really helpful explanation, thanks 🙂

• “Let me show you how do do it”…. *****stops talking, extremely serious face, fast tracking while writing formulae, smile*****

• Accurate af

• suggestions plz for similar formulae

• marry me tooo

• I can only watch your videos pls do more

• Nancy let me know the screen settings, I am interested to arrange the similar screen setting for for my channel. waiting for my channel details

• Best math teacher on Youtube! Pity you don’t have video’s about Fourier Transformations!

• Calculus 2 plsssssssssss

• I can’t solve my question. And my question is how can she write mirrored without any effort? Am I missing any camera tricks?

BTW Niice Video. ! TY :-]

• The image is reversed in post production. Either that or she’s a freak who can write backwards (I can’t rule that out)

• Lol comments are for nerds

• आप का बहुत बहुत शुक्रिया

• Nancy I really thank you for your effort

• very very nice mam

• I love math

• Amazing Calculus and BEAUTIFUL NANCY.

• she’s so hot!

• our children will be smart AND beautiful!

• She’s really good at writing backwards…
And math too. That is also impressive.

((Thanks for the vid, it’s gonna save my life on this calculus exam!))

• She is left handed , I noticed it in this video

• She is left handed and writes backwards

• Thanks a lot..I struggled a lot to understand integration but atlast…(Nobody was ready to tell me cause’ I was just young and small)

• Seriously the best

• superb

• “I know calculus is exactly what you wanted to be doing right now”

Oddly enough, yes lol

• Uriah Siner lol same I’m here cuz I’m actually curious about integration. Also cuz I’m procrastinating about writing an English essay

• This has helped a lot, thank you! 🙂

• Nancy you are the best

• Nancy you look cute af. Can I get your insta?

• Are you Nancy from the Philippines?

• is this woman writing everything backwards

• I have a friend that writes backwards

• For easy way of integration, visit classic mathematics

• @StarDagger Rihannsu 😂😂😂😂😂

• Nah, check out the Expo marker. It’s backwards.

• does she do the part about area under a curve and the actual application of why we might want to do this?

• Is this the basics of calculus? I will be starting calculus in 3 months and I dont understand a thing in this video…

• can you please give more equations including trig in integeration and dervatives. also , what is the integeration and dervatives of tan.

• Don’t you think everyone knows anti derivative is opposite of derivative?Derivative means rate of change of y w.r.t x at any point on the graph.Likewise what anti derivative means?

• mam you are so beautiful

• Nancy you saved my life lol. and youre beautiful! such a calming video. Thank you!

• I passed differential calculus because of you ma’am Nancy, thank you very much.

• very nice.keep it up

• more integral lessons 😊

• it is ‘sick’….lical indeed 12:50-12:59.. calculus is.. lol

• I love you

• thank u!

• She says déjà vu at 4:20?

Coincidence? I think not.

Deja vu
I’ve just been in this place before…

• v+1/v-1 ka integration kaise karna hai

• I have so many questions after watching this . .
Is she writing backwards?
how does it erase like that?
and are you single?

• 9:28 Best enthusiasm I’ve ever heard in my life. You should be an analysis professor 👏👏👏

• thank you soo much nancy! You explain so well. I had mid term and quiz and all i did is watched your videos to clear the concept and it helped me a lot to pass my exams.

• Beauty wid brain.!! Lots of love from India 🇮🇳.!! Thank you Mam.🙏🏻

• Maths and beauty at same place

• Please do a video mam.on the topic “finding the area under the curve by definate integrals” .

• de ja vu

• Where does that 12 come from ?

• 3 hours till calc final, plz save my life

• 韩陈妙妙 good luck ! I have like 18 hours till mine ! Hope you pass your clsss !!! I need a 67 or higher, I need 10 right

• @Julio Carballo too bad, I failed. Good luck on yours

• 韩陈妙妙 dam I got a 100 on mine !!! Luckily my professor was at the tutoring lab and went over the example test questions with me and 2 other classmates , I got luckyyy

• Can you do a video on Riemann sums and definite integrals?

• hot for teacher!

• Dont watch this video in 480 p

• In power rule the value of n can be equal to n=-1

• 😂😃

• Beauty with brains 💖🌹

• your eyes are grey, how you change it??

• Thank u mem…..

• she can teach us maths while writing things backwards what the fuck, yo is she even human?

• I cannot see the board I can see only you 😟

• Te llevaré a casa con mamá :v

• ❤👍

• Math teachers should be ashamed in front of your wonderful teaching methods.

• my first time watching her video… it’s really hard to keep my eyes on mths instead of…well you know..

• So cute

• Integral x^6/(x^12 +1) ?

• Ur mom

• Best explanation!

• Nice nannci mam

• Nice video of math

• U r so beautiful mam ummmahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘

• This really helped me get a better understanding, thanks!

• lmao

• 6:18 welcome to hell

• damn skippy, this really helped out. Thanks Nancy!

• OMG beauty with brain 😛 😛

• hae Nacy? which hand do you use in writing

• How you doin

• PLEASE PLEASE DO CONTENT ON FINDING THE DERIVATIVE OF INTEGRALS!!! I NEED YOU

• Thanks

• I had to like and subscribe.

• Excuse me nancy mem plis tell us how you make videos with technology you used

• No need to apologize for “insulting” with algebra talk. I appreciate that steps and explanations are included. These reminders are helpful sometimes. Another great video . Thanks a lot!

• really u r the best teacher… by ur every video mathematics is getting more interesting for me.

• Sheldine ?

• Get yourself an agent. You have screen presence and authenticity. You can get parts on sci-fi shows, indie films, and tech commercials. The income can support your work. Your agent can use your youtube videos as demos. Good luck!!

• You understood me very well
Thank’s
Love you

• How beautiful! Girl is nice too tho.

• I’ve never found math such beautiful!

• could you go over what integration is for? area under a curve? And how this math is doing that? and what value this has in the area of physics and engineering? thanks

• nancy u kinda of good but i dont get u right ………integration u should work things from de start for easy understanding

• Really just wanna say your channel is AMAZING. you explain things so beautifully. It makes the hardest things simple.

• We should call her Ms. Calculus.

• With this girl narrating I’ll become a mathematician ☺️

• Please make a video on definite integrals🙏💙

• Bro, I still need to know how does she write on the screen? That’s impressive!

• She probably just put a camera behind a glass window or glass “whiteboard’. Then just flip the image and voila.

• probably use front camera

• @NDA ASPIRANT nice

• @NDA ASPIRANT is it correct

• At the fractional part.. is 3/5*x^(5/3)+C a typo? Shouldnt it be 5/3*x^(5/3)+C?

• No, since dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 5/3 = 3/5, so when you take 5/3 out of the fraction (x^5/3)/(5/3)+C it becomes (3/5)*x^(5/3)+C

• Thank you mom

• Hi

• Thank you

• Whoa… OK I know video editing, and it’s pretty obvious how she does the whole backwards writing thing, but the fade at 9:55 has me lost. VERY CLEVER!

• All the time I was only looking at you.

• why

• yes, you are Arabic man

• She to cute I can’t focus!

• Her voice is so satisfying 😍😍😍

• You are really good at explaining how to integrate

• Thank you!!! I was making these much, much harder than they needed to be. (For a year, now.) You and all your videos are greatly appreciated!

• Super

• This is so helpful. I’m starting this topic tomorrow after the Spring break.

• hey nancy.. thanks youve been a great help last year..muah

• I love your video’s , please tell me how to integrate Cos√x/Sinx??????

• That integral has no answer. Make sure if that is the question or if it is sqrt(cosx)/sinx

• @Warc Arden my Friend ,all are telling me that it has no answer ,but why ,please tell me the reason?????

• Justdoit yes it has no answer, I would like to know where you came across this integral. You can tell that is has no solution since there is no function which differentiated which will give cos (sqrtx)/sinx

• 5:15

• You should make a video about how to write backwards. Thanks for all the great content. My Calc grade appreciates it!

• you need to relax yourself lol, XO

• i have learned more from you than all my calculus teaches combined

• Why can’t you be my calculus teacher

• my gf is legit jealous of Nancy. She always gives me a look when she walks into my room and hears Nancy’s sultry voice uttering gently out of my laptop speakers..

• I passed algebra by watching ur videos.now am gonna pass calculus again.thank u👏👏

• Do you make guys Integrate to impress you?

• Thanks

• i dont feel like changing the video for some reason………… must be my love for calculus xD

• nice

• İf you think about it is hard i invite you to search to turkish education system we are in hell…

• I have no idea what are you talking about. I am only 12

• U helped a lot while my teacher doesn’t thanks a lot

• hello…nancy can you help question likes this …. ? please

a company uses two types of raw material i and ii for its product.
if it uses x units of i and y units of ii it can produce u units of finished items where
U(x,y)=8xy+32x+40y-4x^2-6y^2
each units of i costs rm10 and each unit of ii costs rm4. each unit of product can be sold for rm40. how can the company maximize its profits?’

• To me it’s important to give small reminders of algebra steps because it’s a good reminder for a lot of us who forgot how it’s done. I appreciate those reminders, very helpful! The people who end up needing your videos are usually ones with weak algebra skills.

• NancyPi > PatrickJMT

• I swear Nancy will be the reason I get my engineering degree!!

• Bartholomeuw Titus wait this is what ur learning for degree how old r u? I started this properly when I was 15 granted a bit earlier than most would have at school

• @hello there That’s a bit weird, i learnt when i was 15 too , same as you

• where did she get C?????? :L

• Think about it when you’re taking the derivative of a constant it becomes zero, right? So the derivative of x^2+2 = 2x, but what is the antiderivative of 2x? Is it just x^2? What about that 2? When we take the derivative of a constant it just becomes zero so when taking the antiderivative, we need a place holder for all the constants that became zero when taking the derivative

• The only asmr i need

• I’m so glad I found this. I loved Mathbff and this is the best news i’ve gotten all day

• ur beautiful like a pizza 😻

• shes too hot, i cant concentrate

• Watching people doing math while I’m doing math is fun haha..

• WAIT WHAT HAPPENED TO MATHBFF

• As a fellow lefty the amazing thing about your video Nancy is that you are left handed writing backwards on a dry/erase board. That’s real genius right there.

• Im not even studying for calculus but shes making me interested in it again. Damn.

• Hey Nancy I just wanna say thank u bcoz you helped me pass my test. Thank you so much❣️❤️❤️

• Good morning Nancy,I really love your way of teaching, you actually take your time to explained, you are helping me to understand a lot,may God blessed you.

• How do you write backwards o.o

• Why are there no videos on Definite Integrals 🙁

• U teach so well thank u from heart of my bottom

• The first 11:30 of the video: “oh, this is easy!”
The rest of the video: “you know what, I’ll just lose these points in the final”

• and an trying to study them for my final tomorrow and I lost them 🙂

• Omae wa mou shinderu!

• its all easy, im doing triple integrations, and im only 15 nab

• update: got a C. ayyyy good enough for me 😀

• u make me like maths wtf, u saved my exam btw

• I com watch Nancy’s calculus videos and I don’t even have any homework or quizzes due….

• Dan T I’m watching this because I have a final exam tomorrow 😭💔

• I love Trig❤️❤️

• Nancy for president of the USA

• I want to learn how to integrate to win your heart..

• At 2:30 in the morning you sound like you are speaking gibberish 😪 I’m tired. Last 2 exams tomorrow 🎉

• That moment the letters faded out… 9:55 hum. HOW DID U EDIT THAT!?

• u r very fast

• Hey you teach very nice mam

• This is the first video I’ve seen of yours, and I had to subscribe pretty much as soon as it started. I love the way you explain things in a way that’s not too long and drawn out but that is also clear and helps to explain things. When I was in college, I was going for high school education (math), but to become a high school math teacher, you basically have to become an engineer it seems. I never really got the whole Integrals idea. I was so lost in Calc 3 that I switched to middle school education just so I could be done with taking math courses. I’ve always loved math and wanted to learn it though so I’ll definitely be watching your videos and hopefully finally understanding all that stuff I could never get before.

• This video helped me to learn more easily . I liked your teaching method very much. It”s AWESOME!!!!!!!1

• U explain very nice … and I m glad that my classmates don’t know that I study from ur videos and that’s the secret of my good marks in Physics and Maths… thanks for these videos

• Hello
Please what is the integration of
1 /(1-x^2)

• That my friend would be ln(|x+1|) – ln(|x-1|) + C

• I’ve already know what she talks about but why am i still here till the end?

• go and eat something before making any videos u r looking like so weak and sleepy with no energy

• this video literally saved my life!!! Thank you NANCY!!! you ROCK!

• You know all hope is lost if you cannot still understand after being taught by Nancy

• Useful 👌

• your videos are the best …

• I saw that you are missing creepy guy comments on your video so I thought why not … I like how you integrate P.S (seriously … thank you)

• How you able to write like mirror view, you are blessed.

• Hi Nancy, was wondering if you would mind covering double integrals, and double integrals involving polar coordinates please😭. Also triple integrals involving polar coordinates also gave me major problems this semester.

• You’re a very rare person…Smart, pedagogue, beautiful and sweet…A very nice combination indeed…Love from Marseille 🙂

• When you realize the video is mirrored !!

• Owwwwwwwww…
And I was wondering how she managed to write backwards

• People feel more secured when see their mirrored picture

• @Mysterious Mist oh my GOD !!! Was that supposed to be a quote ?!

• Ma’am I have a doubt

• 💜

• LOL

• *You really deserve more subscribers*

• Wonderful instructor! I needed a video like this to help out students that I tutor. (I’m rusty – it’s been years since college!)

• Nancy rel pretty

• this has just helped me wipe away my fears on integration and now i can easily do my test without help nor fear….thanks a lot Nancypi

• thank you so much sister….please make a complete tutorials about integration

• Thanks a lot Nancy <3 you are super! A real inspiration.

• This woman is fake. Its because Maths teachers don’t work for free!

• Nancy !!! Could you show how to solve this form : integral of (x^2 + x + 1)^3/2 . I hope you will teach this form and especially this example.

• Jennifer Van it is the same as the square root of the bracket being cubed if that helps

• How? Are you god? How can you write backwards so good?

• OMG, I love you sooo much, you videos are the only things that are getting me through cal. could you please do some videos on continuities?

• My professor says hi.

• Hi darling nancy

• alex morgan teaches math 😍

• Ok, so I could not take my eyes off her. So can someone teach me Integration for real, right now?

• she is hot. and a mathematician to boot. What could be better

• She’s a tough teacher.
Will not spoon feed you But push you.
These videos motivate me

• Functions i forgot what ever little i knew though

• Really i like you

• Thank you

• Thank u for happy study

• OMG I wanna be married with her, married with her, be my white Pleeease 🙁

• PFFT

• I don’t even know what derivatives are…

• First, I have to past her writing backward that comes out forward.

• all hail the nerd GODDESS!

• Wow a pretty math babe is a true diamond!

• What about S e^mx dx ;m is constant

• Anox YT (e^mx)/m + C

• i love you with these kinds of trig and helping i love so much you are the best in explaning

• <3

• Nancy thanks for your videos! They are very helpful. Can you make some videos on linear algebra topics like vectors, eigenvectors, linear transformation, matrices etc. Cheers

• The introduction of the integration is not clear

• here i see you got a degree and i wish you to take contact with somebody who pay

• You are very nice Nancy!

• That’s maggic when you put it in the calculator and that you compare

• Nancy what do you thik of the little supper?

• verry good Nancy

• You R one of beautiful teacher😘

• First thing i had to do was slow down the video to see if she was actually writing backwards lol i can do it but not effortlessly like that i was gonna say like that would take a lot of practice to do that easily. Anyways she’s not if you slow it down the hand strokes don’t match the letters and numbers written.

• Ma’am,, from where you are??

• Lv y

• she so pretty. Can u be my gf? wish to have a gf like this. hahaha!

• Best thing about these videos is that they don’t waste time,if you get it,you keep watching and if you don’t, you can try another…at least it’s better than waiting for 30min while going no where other than repeating what you already know

• Awesome….

• good
from Japan

• thankyou

This is how you startle people in educational videos

• Thank you so much for this video 😊😊

• apni kon college a poran??kon district??

• @Ahmed Ullah Naogaon Govt, College,apni?

• I LOVE all of your videos and they help so much!! but now that im in Calc 2 its a lot harder to find the information and help that i need! pleeease make more videos soon!

• I’m just perplexed at how she is writing these formulae backwards on a clear screen.

• I suspect you are part of a very dark scheme to make me love algebra.

Bold of you to assume…..

• your videos helped me so much with calculus (got a B, which is better than I thought I could ever do) and now im using them to review calc for calc based physics 🙂 thanks so much!

• I love her please marry me xD

• Bro wtf?!

• That’s it I’m gonna say it,

you fell for it, FOOL!
THIS IS A JOJO REFERENCE
*THUNDER CROSS SPLIT ATTACK*

• cringe

• If my teacher looked like her then I would like Calculus. She is doing a great job explaining though. lol

• J R she was -10 years old when you were 40

• lol! Jesus I’m not that old. I will be 44 in a couple weeks. I am guessing she is in her twenties anyways.

• J R haha haha sorry man! Was too tempting. Was all jokes. Agree with your initial assessment

• A teacher should be like her because explain in a very nice and easy and understanding her is very sample. Good luck π

• Well she’s hot smart and funny damnnnnnn

• Please make Calc 2 videos, you are amazing !!!!

• U are good

• 6:16 clicks off video

• Looks horrible. Really isn’t difficult at that point… Yet…. Just tedious

• Loved ur videos
Can u do a video on vector multiplication

6:34 board after 30 seconds of not paying attention

• underrated comment

• That’s how I feel actually in class.

• 😂😂😂

• HAHAHAHAHA

• Hey Nancy ,
Ya gotta be a boolean woman. And or every now and then
…..😜

• Thank you !

• u r awesome

• I LOVE Calculus 😉 Your presentation/video makes Calculus more entertaining and understanding 😎

• Feel free to insult,I have no pride when it comes to math.

• the way she talks when she’s teaching and her facial expressions gives me anxiety :/

• I understand with the help of your cute learning wishd you were gf😄. Sorry emotions flow

• WOW!!! THAT CLEARED MY 2 YEARS OF DOUBT!!!
CHANGED MY YEAR!!!
THAANKS!!!

• 1:52
Wait, I’m sorry, but did you just write *backwards*??

• Wow. No way! I finally understand! Now I won’t fail my test tomorrow. Thank you so much!!🤗

• you make maths easy and lovable…wish you were my lecture

• What happened at 1:15?

• nahi samja

• This is so confusing for someone who doesn’t know anything about this.. is her left my left or right?????

• Omg mirror writing…

• I cant understand integal -Nanci

• You read my mind at 10:21. Thank you for that warning!

• You teach very well and precise.

• 😍

• Can you be my mom?

• Are you sure you mean mom? Maybe gf??

• Great

• I WISH BOOKS ( AND MOST TEACHERS). WOULD EXPLAIN THINGS AS YOU DO NANCY.. HAVING TEACHERS IN MY FAMILY MYSELF I HAVE NEVER FORGOTTEN WHAT MY NEPHEW WHO TAUGHT 39 ——YES 39 -NOT A MISPRINT COMPUTER COURSES BEFORE HE DIED AFTER A LEGTHY IlLLNESS USED TO SAY. “ THE AVERAGE PERSON CAN LEARN ANYTHING IF THE SUBJECT MATTER IS EXPLAINED RIGHT”. AS FOR MYSELF I AM JUST HAPPY TO READ MY BIBLE IN OVER 12 LANGUAGES INCLUDING CHINESE ETC. —-EVEN THOUGH I TOOK SOME CALCULUS IN UNIVERSITY BUT NEVER REALLY KNEW WHAT I WAS DOING! !!! I HAVE TO SHAKE YOUR HAND ONE DAY ,,,

• Nancy,
You are a left handed genius. You make this math look easy. Two formulas only per page of notebook.

• i had to think for a solid 10 seconds if she was actually writing backwards this good

• Lol

• i love you

• I’ve been watching the portion about negative, root, and fractional powers for the last hour. Everything up to that point I understand. When it gets to that point I’m just lost.

• Same bro I got an exam today I’m screwed 😭

• Amazing technique

• I just need to watch your videos for a few seconds and I get concept!!!! You are 1 in a billion girl! Thank you and keeping making these videos. You are truly proving a public service to students.

• Starts doing calculus forwards….

• very nyc nancy

• You saved me again. Thank you😉

• does she write fucking backward bro?

• Can n= -2?

• i am starting like math because teacher is so hot😂😂😂😂

• where are u from? i wanna meet u…!

• wish this girl was my math teacher.

• Just want to say thank you for your incredibly helpful videos! I literally find myself walking around my campus at 3:00am cramming calculus the day before my exam. ( And actually pulling it off thanks to you! )

• Im sorry I dont watch your videos because I wont pay attention to the math.

• Literally doing a chemistry degree and these videos are a lifesaver

• Great video nancy♥️♥️♥️

• I love you

• Whelp. I am back here again a year later. Currently trying to figure out why *Integral sign dt = t + C*

• I want you to insult me with all of the algebra and trig math pointers that you possibly can.

• 6:14

Alright i’m dropping out of college

• Many people do trig and begin calculus in high school. 🙁

• dude same

• Can’t concentrate on math while looking at u

• One solves the integrals c plus bx power mainesh _3 /2 intoo dx

• Hi Nancy, I love Math. I really enjoy Calculus, but I am struggling with it. I still love it and enjoy it though. Your videos help a lot.

• I pass my pr-calculus b/c of her

• yo shes so hot

• If shes writing on glass it should be backwards for us, I think shes flipping the video so it counteracts, shes also probably right handed as she appears left handed in the flipped video

• 5:50 is it tho?

• TQ

• Amazing♥️

• Thank you very much♥️

• +

• if dx.dy=1 whats the solution????anyone?

• bravo

• Subbed ’cause… I’m superficial. It’s just so soothing to see an intelligent hottie explaining things she love.
Wish I had this attitude towards studies in general. But at 42 years old, what can be done if not just watch YT videos like these?

Scroll down, there’s nothing else to read, or just continue watching this grace in motion. 🥰

• چقد استرس داری تو آروم باش ، بیخیال دنیا و قانونهاش😅

• Hello Nancy, if by chance you read the comments : I’m sure, like myself, many would appreciate if you could number your videos, or if at this point it’s too much trouble to rename existing videos, perhaps make a very short video / add it in description somewhere, to give the best sequence in which to watch your videos (many are self-explanatory, though some cases aren’t that clear). To be honest, your videos may be the best math teaching videos, and I’ve watched a good number of different channels’.

• If she had been my math teacher, paying attention would have been a serious problem.

• Dear Nancy, there are a lot of “invisibility” in math, and assumptions, ……no wonder I couldn’t wrap my tiny brain around it!
However, Differentiation & Integration and all the courses leading to it in my senior high school year, were my favorite. I also had a very good teacher! Mind you though I learned everything in Arabic lexicon. For the fun of it, although recalling is painfully slow and fragmented, I’m intrigued to hear you explain it in English😊

• In other words, women are better teachers and educators than most Machos, Salute 🙏

• i can listen to your voice for hours. thanks for doing this 🙂 the world is a better place 🙂

• Should briefly mention that the +C is only for indefinite integrals (Integral sign with no super/subscript). Don’t need to know more about definites yet, but important to mention so that rule sticks better.

• Can you make a video on numerical integration

• Hrllo,teacher excellent video

• She sounds so insecure…

• I wish u were my school ‘s maths teacher. Cause what ever my maths teacher teaches it feels like even he himself is confused and standing in front of white board to clear our doubts

• Please make more Calc videos!

• You are very helpful! Thank you so much ! 🙂

• Thank you Nancy!!!

• I love your videos because I fall in love at the same time I understand my assignments

• I love learning math from beautiful women

• I send u a kiss baby :*

• I love your teaching skills Nancy p

• I feel so dumb watching this .

• I’m sorry, but I can’t listen to a pretty young lady explaining shit to me. I already have women teachers in chemistry, algebra, and geometry and its tough, but this is just too much. Too pretty, Im legit sorry xD

• 11:25

• Haye She is my Maths Teacher 😍❤

• is she high or what

• you legit just saved me. not just from failing maths. but from life.

• hei nancy ,your video is really good, thanks. it helps me very much

• Can we say that integration is opposite of derivatives

• it’s really hard for me to concentrate on your videos giving my weakness for beautiful women..

• Do I have to look that pretty to be a math expert?

• Thankyou!!! Nancy Pi.You are really a good teacher.

• 500

• I.. finally..get it. Integrals give you amnesia

• Nancy is so goddess-tier

• You are so cute and intriguing Nancy!

• And I am glad you know Mathematics. I am also into the subject.

• chhhaaaai,Nancy ,you are bae;

• Just subscribed to NancyPi, would you do the same for me?

• Fantastic Explanation really enjoyed..

• You are so beautiful i can’t concentrate on what you are saying… 😁🙂

• Déja vu is my fav part pls keep up Nancy always the beest loove u my beest icooniic teacher❤❤💓💓😻👭👭👭

• 💎💎💋💗😇😇👑👑😎

• I have not studied limits and functions in detail. How can I improve myself in integration and differentiation- from which level should I start? I want to understand the two operations with applications in science and businesses.

• area function from axis

• Could you tutor me?

• I dont get the answer from the “More algebra” expansion. Is it so that the 3X^2 is 3/3 × X^2 = X × X^2 = X^3? 😂

• Hi,much to say to thee,thanx,bliss, XAMichael XAMBUNJILOM

• If she was my College professor, I wouldn’t miss a single class

• Awesome video

• what is math

• I love the whoosing sound when Nancy is writing super fast

• you are so sexy…

• I always have 2 questions when it comes to this high end math: 1) why does the answer still look like a problem needing to be solved? 2) what is the real world application?

• I have the same questions some books that claim the actual usage and applications for calculus fail to demonstrate how they work in a low level, I assume that’s why so many people fail/drop calculus entirely.

• ضاع عمري على السلمي ونصير وعبدول 💔

• Good for both education and sight😂😂

• Packers Andrew wilhelm 12

• Good Teacher Maths.

• i dont like how was writes it out first and then explain

• How can I focus 😭

• easy

• Thankyou Nancy

• All through this video, i asked myself how she writes inversed.

• Gorgeous and love math. My dream woman

• Please will you marry me haha

• I bet you are record a video, and then mirror it. So originally you stand on the right. Am i right?

• Thank you from the bottom of my heart. <3 Because of your great tutorials, I passed my calculus exam and got my network engineering degree 🙂

• Imagine your math teacher explaining some difficult math stuff with a smile on his/her face

• impossible.

• Does anybody know how she writes in a transparent board?

• I love you

• ME: * takes deep breath of relief * The worst is almost over
NancyPi: 6:12

• Is that Aubrey Plaza?

• Nancy I really love you and your channel

• Wow, awesome video, since then that I watch it, I was inspired to create my own video tutorial. I hope you enjoy my discussion too. If you have some inquiry. You can visit my youtube channel too, for some video tutorial.

• How to do this kind of video effect

• this helps a lot, thanks!!

• Thank you Sister

• Thank you Nancy. You made a difference to my learning journey

• 6:15 yep ill just switch to arts degree

• Nancy, in order to understand math Better pls write on the board line by line and explain and do not write the whole line in one second. this makes people hard to understand. ok thanks

• How can make this video?

• What is the program used to make this video?

• What is she writing on?

• thanks
this helps

• oh my gosh, it’s like she’s writing on my computer screen.

• She is so cute🥰🥰

• Thank you for helping me get through college!

• I don’t know which do i watch u or integration:3

• Thank you!!You are a great teacher and it’s really easy to understand your explanations.I am really grateful!🙂

• She’s smart af

• Yeah I think I’ll just drop out.

• How do you make a video? It’s so cool. Do you use a whiteboard or write on the screen?

• Very good

• Good stuff. This was inspired me !!

• that’s a lot of writing.

• “I don’t want to insult you”

You are not insulting me. My college wants me to take a course on mechanics even though design – my major- should come under arts. I didn’t bother with calculus much in 10th and I barely passed junior college. I am watching a youtube video because I am dumb. The professor’s notes are made under the presumption that the student studied some stuff in school.

• @Gaming Student appreciate it mate

• What would I use this for in real life

• You just made me pass calculus
Love you

• I am going into 10th grade and understood this. Thanks!! I now I love math even more!

• WHO ALL ARE PREPARING FOR IIT?
LIKE!!

• FOR WRITING WHICH BOARD YOU ARE USING

• Don’t tell me, you learn how to write backwards?

• thank you I understand now

• nice

• Its me jereely

• Oh my goodness who else remembers the MathBFF days? 🙌🏿🥺

• This is a very helpful and straightforward video.

• I started an MSc in applied economics recently and these videos are a lifesaver.

• What is the use of Integration and differentiation….can you pls tell that….When should we use them to find what…..I am not getting proper answer from internet…😭😭😭😭😭..pls pls

• I’m still alert because math is amazing

• wow, you just summed up my last two weeks of confusion and made it seem like nothing! you’re amazing!

• I love your tutorials on calculus, God bless you

• Hi Nancy, is your last name actually Pi?

• THANKS A LOT NANCY !!!! APPRECIATE THE CAPTIONS TOO.

• Great work Nancy..

• مدرسه في قمة الابداع درست عليج لعام
ولحمداللله طلعت صفر برياضيات

• you are very cute

• Am I the only person who just stared at her the whole video? Why she so hot…. I accuse all math teachers that are hot af, they make me fail math tests.

• i get the point

• thanks

• @bente schoone

• Great mam

• If its possible then see my channel

• Me + u

• Hi Nancy …. Realy i lik the way how you introduce you idea…that is great way to do that,me too iam professor of math,iam frome morocco,technicly i have a question, haw can i do lik this…i wanna write on the glass lik you but i don’t know how can i do that….if you can giving some helpe..just do it..cause i need it..thanks for you’re response

• How do you find the C?

• Your videos are helping me a lot! Thank you so much!!!

• Her explanatory power is pretty weak.

• No one:
Really no one:
NancyPi: 6:12

• Ever body keeps saying she rights backwards she is left handed

• خوش شرح بس مو افضل من حيدر وليد 😃

• NUR POLITIKER wollen INTEGRIEREN. Wer das Wesen Mensch kennt der weis das KEINER integriertvwerden will. Es gibt’s das sich Leute selber integrieren. Wenn Die eben in ein Land wie Israel oder den USA einwandern gibt sich jeder Mühe. Aber normal bei uns will jeder bleiben wie er ist und nur Kohle verdienen. Hört endlich mit diesem Blöfsinn auf. Es gibt NUR KONFLIKTE und je länger umso scjlimmer. Politiker sind keine Ethnologen.

• sexy math teacher you are helping the universe thank you

• Am here during this pandemic (covid-19) your videos are helping alot since we’re at home not going to school

• She is indeed a beauty with brains.
I liked her teaching style like how she smiled throughout the video while teaching this difficult concept of Calculus.

• You seem like the kind of teacher who has to do those friendly reminders for the kids who are forced to take this class, and you know that even though you’re saying it now, those kids will not remember it when they go to integrate.

• It feels like just keep listening you😊

• Guyz you are in a delusion,go check out math videos from Eddie woo youtube channel,I assure they are 100 times bettet than hers.Nancy teaches what,just the rules to gets marks but eddie teaches the beauty of maths through how.She is not humble as him ,he is a great teacher

• I think I’m in love

• Very good teacher.You are an inspiration to girls

• Why at 11:18 does she write 6x^0 instead of to the power of 1?

• Meme wange you seem shy

• okay so she’s perfect and beautiful

• She’s an android math bot. Every once in a while, she engages fast forward.

• everything was fine and then 6:11 happens.