# Trig Substitution… How? (NancyPi)

237,014
Published on October 16, 2018 by

For my video on how to do BASIC INTEGRATION, jump to: https://youtu.be/e1nxhJQyLYI
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

HOW TO KNOW WHICH trig substitution to use: If the x-expression under the radical has the form of "a number minus an x^2 term", then you'll use a SINE substitution. If it has the reversed form of "an x^2 term minus a number", then you'll use a SECANT substitution. And finally, if the expression under the root is addition (the form of "an x^2 term plus a number"), you'll use a TANGENT substitution for the problem.

WHEN to use TRIG SUB: If you have an integral with a radical expression in it, and you know you cannot integrate using: a Table of Integrals integration rule, or using U-Substitution, or using the Power Rule, or using other integration techniques like Integration by Parts or Partial Fractions, then it is a good idea to try trig substitution.

HOW TO DO TRIG SUB. Here are the main steps of trig sub problems: 1) Decide which trig substitution you need [x = asin(theta), x = atan(theta), or x = asec(theta)], filling in the value for "a". 2) Simplify the radical expression by plugging in your substitution for x in the radical [For example, for a sin sub, plug in for x in sqrt(a^2-x^2)]. 3) Find dx from your x substitution. 4) Substitute into the original integral, replacing the radical, the dx, and any other x factors, with the theta expressions you found. 5) Simplify and integrate, using whatever technique you have to use. 6) After you integrate, it's still in terms of theta. So the last step is to get it all back in terms of x. Draw a right triangle off to the side, label the sides with what you know from your trig substitution expression, find the third side, and use the sides of the triangle to get an expression for whatever trig function you need in your final answer.

For more of my calculus antiderivative, indefinite integral, definite integral, and derivative math videos, as well as more examples and help with integration rules, using an integral table, integration formulas, trig integrals, completing the square, and a review of right triangle trigonometry, check out: http://nancypi.com

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• First ❤

• Please make videos on solving trigonometry equation and proving identities..

• This is my favorite Nancy outfit.

• @Dejen Gebrezgabiher What’s the problem

• @John Smith you own Nancy outfits?

• Dejen Gebrezgabiher TELL US THE GODDAMN PROBLEM

• @Dejen Gebrezgabiher whats the problem wtf man cant just leave us nerds hangin

• Dejen Gebrezgabiher it’s probably pointless to ask after a year, but what’s the problem??

• Perfect timing!

• Trig-sub

Ha! I’m a cool kid now!

• Great vid 😊

• I never saw this video but thank you for posting this up!
Can you please upload the application of Integration. For example, The disk method and shell method.

• What If the Number That Is ‘a’ Is Not A Perfect Square For Sin Substitution?????

• Just keep it as a square root.

• Thank You

• Easy like eating foods

• This is better than Netflix.

• I needed this like last month 🙁

• Coincidentally, I have my exam tomorrow morning lol. You are very helpful, thank you so much Nancy!

• I’m replacing my x’s…trust me ^^ super great video as always

• Hi Nancy

• The first time I saw this in class my head exploded. I watched the lecture again and it clicked. Thankfully we were allowed to use the formulas for the exam.

• Hey Nancy! Again awesome Vid. Would you like to concider doing a video about solving improper integrals? They are somewhat still confusing and they fit really well with your arsenal of integration and asymptote video’s!

• 7:50 “cluster-f*ck”

• hmmm

• a mathematician using the word coincidence , has the universe just inverted ,,, , that’s just evil : )

• 7:50 also a mathematician using the word “cluster-f*ck”

• that’s code for trig sub so is trig sub code for cluster f ,,, jusy dont watch is straight after reading that

• Awesome I love your shirt.

• “I know this is a bit of a cluster-f*ck” ICONIC and SAVAGE

• 7:50

• yeah, it’s intense…

• like a math Megan Fox

• better

• minus the surgeries and strange thumbs

• Women do think…

• Except she can actually do what she does well lol

• True

• U are amazing. Thanks

• Very good thanks more but can you make a video about geometry please l have a lot of difficulty

• Senpai pls

• You should do some ‘adult swim’ math videos with more swearing, I really enjoyed you describing the first solution as a clusterfuck

• hey whats poppin, i got a question…how do you do them derivatives of a trig function and also how do you do those rate of change/velocity questions. Thanks homie.

• I love the comments on these videos. So unprofessional but so intelligent. Autism in it’s purest form.

• @Juice how can you just assume someone has autism?

• @claire li Because they get very triggered when you call it out.

• @Juice this guy hasn’t made a response so too quick to judge?

• OUCH!

• I’m not a maths student

• Me neither but PHYSICS :c

• Or English, obviously 😂😂😂

• @Twobarpsi It’s ok to say maths instead of math.

• @MR YUP no

• @Twobarpsi they’re actually speaking better English than you

• I assume all of this can be used to work out the date the universe will implode on?

• James Parlane at least it’d be useful 🤷‍♀️

• You’re right…that was intense!

• YOU ARE MORE ATTRACTIVE THAN YOUR LECTURE 🙂

• 7:51 excuse me? Did I hear right?

• @PikPobedy Yeah, cuntservatards sure get worked up over the smallest things.

• lol a nice little laugh after finally understanding this.

• The Mad Titan I don’t know, if you turn on the “official” captions, you get something hilarious.

• suddenly…
I’m HOT FOR Teacher

• Nancy naughty lol. I had to go back to make sure I heard her correctly.

• Thanks Nancy – I always found trig subs super difficult but you explained it really clearly. You’ve definitely filled in the gaps for me – I think I’ll need a lot of practice but your video is amazing help! – thank you!

• Series and Infinite Series? 🤔

• yo nancy wheres nancy merch

• yea we need merch NOW

• I love you Nancy. You are really my heroine in my time of need#calculus2

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• Haha

• best math tutor online. we all know why.

• You are my hero. Love all your videos, but I probably need this one most!

• hi (sorry for bad math)

• Hey could you do a video on maximum + minimum calculus? inflection points? 🙂

• Wait, I’m confused about the video. So the cops knew that internal affairs were setting them up?

• I wish you would have uploaded this video a little bit earlier.

I just had my test on this topic.

• cluster what? that was to funny.. I think I learning something. thank you. you are a good teacher.

• uploaded 2 days before my quiz on this holy shit

• i’m a good listener. that made me feel stupid.

• Thank you Nancy.

• You explain math very well but I am still scratching my head on this. I love the basics of trig but the deep stuff just flies way above my head.

• Clark Huppert it took me a second time watching the lectures to understand also just give it a go.

• @manuel zimmerschied
Thank you Manny I will go through it again. I appreciate her style of instruction. She definitely knows her stuff.

• Can u plz solve exact and non-exact equations cuz i like the way off your teaching u have amazing skills and u r easy to understand

• Thank you

• I already know how to integrate but see your videos because I love you!

• You was in mathbff before?

• plz have my kids

• like*

• so attractive

• I love you ❤ Nancy

• thanks, so happy this is up I have a calc 2 exam this week

• shouldn’t dx be equal to -6sinΘ ?

• Mike Donnelly dx is the derivative of 6sinO (d/dx sin x = cos x ; and you keep 6 since it’s a constant)

• You are very hot

• “it’s a bit of a cluster fuck” haha, love it!

• LITERALLY UPLOADED JUST IN TIME FOR MY EXAM TY ILY

• can you do polygon pls..

• I hope that I was the cosine ❤️

• NANCY PLEASE UPLOAD MATRICES AND DETERMINANTS AS WELL AS SEQUENCES AND SERIES. I NEED YOUR HELP

• Hey Nancy, I would love it if you did a video on series, and different tests that you use (Divergence Test, Ratio Test, etc.) to find the convergence or divergence. That’s my main struggle.

• Cluster what?

• Hi, Nancy! I love your videos!! I was wondering if you could do some optimization and l’hospital examples. My exam is coming up on nov 9th. D: Also, some antiderivative examples for an other video maybe? That’s our next topic after the exam.

• Bonjour, eest ce que vous parlez un peu le francais, Cordialement. Patrick

• Please marry me! haha You are the best TY goddess !

• Nancy you aren’t making vids. Im waitin. Make a video on alevel functions plz im having trouble with that.

• To uncluster 7:53’s fuck. Use Euler’s formula [ e^ix = cos(x) + i*sin(x) and e^-ix = cos(x) – i*sin(x) ] to turn trig functions into exponentials.
i = sqrt(-1):
sin^2(x) = ((e^ix-e^-ix)/2i)^2= -1/4(e^2ix -2 + e^-2ix). Exponent integration just follow power rules, easy peasy.

Eulers is like shorthand for sinusoidal functions when it comes to powers or sqrts or inverse trig functions.
If your professor gives you a 0 because you used different techniques than they have taught 😻. If they write a one line integral that takes an 8×11 college rule sheet single spaced, to answer, bring a case of beer to the next exam and get everyone to write hollywood style gibberish on their exams.

• Very useful video,dear Nancy please make video on limit of sequences

• Can you make a video regarding Logarithmic Differentiation and Related Rates? Please? I am currently struggling for my upcoming Calc Test.

• I really do love you

• 10:17 How did 36 become 18 ?

• shouldn’t it be (theta -(sin2theta/2)^2 +c??

• liked because of the clusterfuck

• Thank you so much for this video @nancypi, would you please cover improper integrals asap?

• ~7:41 hmm. I would have loved to have seen your notebooks when you were in school. Regardless that it is obvious that you can derive what you need… you also have a shitload of identities tucked up in them brains. Who would have known that multiplying by one would be so important!?!!

• I just watch couse your hot

• 7:51
Did she just say “cluster-fuck”
i’ve never heard her use a cuss word before.
amazing

• If you turn on captions, (not the auto generated one) is says she cursed

• I thought she said “this is a little bit of a cluster but…”

• It was at 7:55 and she’s right.

• That’s what trig sub’ll do to a person.

• OH my gosh NANCY!

• I don’t know if the student teacher policy exists through youtube. PLEASE GO OUT WITH ME! one date.

• Can you do a video on integrals by partial fractions or integrals using double integration by parts

• nancy will you marry me???

• Awesome!! I get it, YOU TEACH VERY NICE.

• The steps you use are ordered and with a lovely touch

• I love The Trig and I like you too.

• Can you please do some topics that’s going to be on Calc 2 and Calc 3

• you ever want a hot math teacher. well this is her

• you are realy feel us 😍

• Can you do a video on Riemann Sum ?

• Your voice and energy are so damn comforting. Are you like 27 years old ? You have a master is mathematics ?

• Hi nancy! Do you have any episodes on Taylor series?

• I’m not even in this class yet. Rip

• Nancy i love you

• Can you make more calculus videos 🙏🏼 past derivatives & implicit differentiation. Such as related rates? Or derivatives of inverse functions?

• watch my video for all types of Differentiation Problems

• kumar upendra it says your channel has no videos …….

• Areas and Integration pleaseeee thanks!

• I am still waiting. Plz make a video on cie alevel functions topic.

• Your are my good tutor Nancy. More grease to your elbow…

• *She is a complete pack.*

• *I can’t handle such intense classes*

• Get a room…
For yourself.

• Could you do one on partial fraction decomp?

• You are so beautiful then how can I concentrate on question 😘😘

• you talking a lot ,

• Please result of here what is?
lim 1-cos3x/x^2
x–>0

• Thank you so much. You are the best math teacher I found online.

• If you have time, could you make some video about probability? Thank you so much

• Question where can we ask you math question? Like how and when to do the chain rule with product rule.

• 16:03 “Some people use ‘you’ “ 😢 lol

• Haha yes that was funny!

• question – even when you can use more than one method to solve problems (trig sub, u/v sub, etc.) would it be better to just master trig sub and to use it even when you can use other methods (at least until you master it)? My thinking is that if you have trig sub down like an old habit you won’t get thrown for a loop when you get a problem that requires it. If you have it mastered, then learn the easier methods. Past experience with other math course is that sometimes we get used to just solving the problems quick and clean then when we need a more complex method that we haven’t practiced….screwed.

It is a bit brute-force for awhile. What are your thoughts?

• ah Nancy your videos are so great! saving me in calc bc

• Shes so pretty

• I had so much fun watching this Nancy chick 😛💗

• well, you are skipping a lot of steps i cant understand 17:40

• Before I watch your videos , I like them first

• Excellent explanation of this technique using good examples. Very helpful and insightful for me. Thanks Nancy!

• love of my life

• Can you make more integral calculus videos

• Exactly I love you although I don’t know where are you …..

• Thanks Nancy! Saved me right before finals :’)

• this stupid shit is driving me insane, wouldn’t wish this upon my worst enemy

• great teaching. .. Nancy I love you … plz contact me Whatsapp +923369769880

• “I’ll be right by your side….”Prof during final: “Who is this?”

• seems legit

• C’mon it’s Nancy! Everybody knows Nancy

• @Patrick Bossome Is it true that she was born in a cherokee tribe and was kidnaped by a pastor at the age of 3?

• I would mess my trousers if this girl was even five feet infront of me she is so dreamy

• @Jeremiah Carr Yikes…

• when im doing my homework and trying to write stuff down quickly i make the little whizzing noise like in ur videos when you write stuff down

• You’re amazing Nancy how you write mirror image with left hand 🙂 Did that take a lot of practice? I’d love to see a video on how you do that.

And your math tutorials are the best! Especially the more complicated ones. Just the right depth for practice. Keep up the great work!

• A M Salim she writes is normally and mirrors the video. If she didn’t mirror the video we’d be seeing/reading it backwards.

• Its really cringey seeing these thirsty people comment on nancys looks. Get over it, relax.

• Brandon Brea exactly I was thinking I’m in high school and doing this and I’m nothing special yet this guy is reviewing trig sub for engineering?

• @Username HAHA, well said, regarding @alb12345672.

• U GAY

• literally. like she’s just doing her job.

• probably all from muslim countries where women are outlawed.

• Nancy for president👆

• Oh awesome! This helped me a ton. Thank you!!!!!!! P.S. you totally won me over at 7:51 lol

• you the best…i like that girls prove to guys wrong… that girls can also do better than boys

• Кто дрочит на это? Ставь лайк))

• I hated trig substitution back in college. This is worse than I remembered. I can’t believe I made through calc 2.

• Clusterfuck indeed

• how can you write like that? Are super genius like 200 IQ???

• Nancy almost seems to have elastic arms. Look at how far that girl can reach. I think the writing backwards part must be a software trick, although, I had one professor who could write with both hands at the same time, both sides of the equations went up at the same time with the result that NO ONE IN THE CLASS could ever keep up.
Thanks Nancy…You make it all much more interesting, and thank you for the candor…YES, we all use tables whenever we can. I’ve lugged Abramowitz and Stegun into more than one open book final exam.

• Hello! at 7:22 why can’t you rewrite sin^2 theta as (1-cos^2theta) and just use U sub? If anyone can explain i’d really appreciate it thanks!

• 20:45 can someone explain what happened?

• Yes

• You are Soo beautiful

• you beautiful we should hang out together miss

• no shes mine
.

• @NancyPi, I like your sarcasm at 5:37. Thank you for these videos. I learned these things many years ago, so this is a refresher for me. I have no purpose for it other than pure interest. Yours are my favorite. I like the pacing and format. You’re also extremely easy on the eyes 😉

• She is quite excellent writing backwards. Also try Paul Dawkins calc notes.

• Hii nancy…

• Complete pack…

• Thank you so much……. God bless you mem

• Clusterfuck

• Good explanation. You had me at “clusterfuck”. 😉

• Are you a school teacher by any chance?

• For the sec sub, as the radical is the denominator, should we consider the domain of the integrand?
What if multiplying x with the radical?
thanks.

• At 2:12 that integral can be done by partial fractions (no need for inverse hyperbolic trig functions there).

• is it only me that is amazed that she can write backwards??

• Your saving my life and my degree 😂

• integration makes me wanna kill my self

• What a legend! Thank you for helping

• You are a perfect 10 out of 7

• Liked just for 7:51 because that’s how I’m feeling after getting a 68 on my first calc 2 exam.

• Bet the class avg was a 40. So good job! You’ll make it. Trust the curve (if your prof is nice enough to appoint one!)

• Basically you are changing the basis of integration from x to theta. This is a lot easier to explain if you use the triangle to explain it first, and then show it in practice.

• Nancy I lv u….

• I can legit focus on this video really well. My prof has a greek accent so it’s sometimes hard to hear and pay attention to what he’s saying but this is really really great! Thanks for the upload Nancy!

• Great video and effective way of explaining it.

• Keep on making maths videos….you will help a lot in increasing worlds average IQ

• In first example sin substitution the finale answer I think instead of x/2 should be x/36 because 6×6 is equal to 36 thank you so mush 🙏❤

• Oh I realize you make 36÷18 and equal to 2 tnx for your help 🙏❤

• Partial Fraction Integration keeps tricking me up, any suggestions?

• whenever you say “Okay, let me help you out.”, my spidey sense tells me I’m not going to understand what you are about to write

• u r great …i lyk ua teaching

• Nice

• i didnt even see what she was writing

• I dont know how i end up here but i dont regret😍

• I’m sorry…There was calculus in this video?

• Nancy you made calculus 1 easy for me… now i am taking cal 2.. and i have no clue how to do it without you… please make it soon

• When she says “don’t be scared of the trig,” it sounds like she’s saying it to herself as much as she’s saying it to us…

• Thank god you wrote the rules, I was not prepared to research those and my professor didn’t show my class like 50% of them -_-

• 15:00 You can actually do it without trig sub.
Rewrite it as root(25+4/x^2)/x^3
Essentially moving an x term from the denominator into the root.
Now, let the part inside the root equal to u.
On differentiating u, we get -8/x^3
Multiply and divide the integral by -8
Solve the rest using u substitution

• 5:37🤔

• Sexy lovely beautiful and professional tutor 🌹🌹🌹🌹🌹♥️♥️♥️♥️

• Not to be weird, but she is pretty. Don’t even @ me.

• At 13:19 where did the – (x/2) come from?

• cus sin(θ) = x/6 and cos(θ) = sqrt(36-x^2)/6
you have 18*(θ-sinθ*cosθ),
multiplying 18*(-sinθ*cosθ) =
=(18)*(-x/6)*(sqrt(36-x^2)/6)
or (18/36)*(-x)*(sqrt(36-x^2)) and 18/36=1/2
so (-x/2)*(sqrt(36-x^2))

• Charlie Foxtrot

• for god sake please stop smilling!!!
I cant concentrate !!!!
someone pls help!!!

• Hey Nancy, You made a mistake. at 14:37, your final answer has an x/2 where an x/6 should be. I think, that is if sin(theta)=x/6.

• I thought the same thing. Wouldn’t the sqrt(36-x^2) also be /6 if cos(theta) = sqrt(36-x^2)/6.

• @Robert Stone 36/18 =2

• Do you make calc II vids?

• OK ! Let’s be honest: Trig substitution is a difficult stuff. There are a lot of rules, a lot formulas to know by heart, a lot of tinkering around…
But you certainly did a great job in covering a lot of it in a really understandable and helpful manner.
This video should be seen several times until it is all sinks in !

• I threw her a like the moment she said “clusterfuck”. Amazing

• Im more impressed on how you can do this writing backwards!

• She doesn’t. She uses a simple trick but wants it to be a secret

• Nancy, you did a great job

• You are very beautiful

• Your class is also effective

• Nice class

• Great job nancy .love you from india

• Where r you from?

• I want follow you directly

• Theres always a big inhale with nancy videos xD

• nancy pi deepfake in the works

• How did you get 125/ 4 in example 2 at the 18 minute point?

• right? I cant figure that out

• wait! I got it!

ok so on the denominator you see the term (2/5*tantheta)^4 right?

So take (2/5)^4 and you will get 16/625, so because this is in the denominator to flip it to multiply wiht the 2/1 and 2/5 term you flip it to be 625/16.

now simplify (2/1)(2/5)(625/16) = 2500/80, simplify this by a factor of 20 and get 125/4

Hope that helps!

• I would never miss your class if you were my teacher😍

• You look like my crush😍🔥🔥

• Trig substitution was definitely the trickiest thing for me. With your explanations however it all makes sense. You are a superb teacher. Thanks.

• Very informative thnx!

• You explain so well! Thank you!

• How she write on the board?!

• 20:47 can someone please explain to me what happened here? i am lost huhuhu

• u = sinΦ
you will then use the power rule to help integrate 1/u^4

• A beautiful woman who describes a grouping of trig integrals as a clusterfuck has a very bright future in teaching! I, for one, will forever be your disciple.

• Please teach me the proof of Fermat Last Theorem.

• i love you

• *I wish this would have happened **0:13*
*You were by my side.* 😍

• Why is the denominator of the last problem just a normal square root instead cubed square root?

• Your mesmerizing look causes distraction in my concentration towards math..😆😆😆😆

• Oh my hru nancy? Fancy Nancy 1+1= 3;) if u n me

• And I thought Chinese was a hard language.

• I had to turn on captions to confirm what I heard at 7:50

• I suddenly enjoy trig sub integrals.

• Haven’t seen anyone mention it, but I love that background hum when you speed up your videos.

• That sound is strangely satisfying. Lol

• Me too!!!!

• Nancy doesn’t seem to like trig.

• thank you thank you thank you thank you thank you thank you thank you thank you

• Question here, why do you replace x with theta in dx at 6:05. I know you got to rewrite everything in order to be in terms of theta I just do not understand how you have got this expression 6cosΘdΘ, especially dΘ at the end 6cosΘ is x that I know.

I understand everything else perfectly though, outstanding lessons thank you Very Very much Nancy world needs more people of your kind!❤️🤓

• You already have written that 6cosø = sqrt(36-x^2) so you dont need the triangle to figure out cosø = sqrt(36-x^2)/6 just saying

• Nancy is, by far, the prettiest and hottest teacher ever.

• 20:54 “Use the power rule to integrate…” I’m not sure what you mean here. Wouldn’t u-substitution be more effective?

• it’s a u-sub then the power rule. She skipped the steps.

• Got it. Thanks!

• Why se use trignometric function in integration , madam specify extensively.

• There is never ever been a cool kid that has said “trig sub”…

• teddysurf Yes there has been. She just did it.

• Samuel Feaster lol

• Pls stop more talking I cant wait the calculation

• Can you use trigonometric substitution to differentiate?

• I have my second wind this is a cool class 👌😎 thanks 😊

• Please how to integrate (a/1-a)^5/4 da ?

• I thought I was quite decent in math. Nope, apparently not… Didn’t got anything of what she said… 🙁

• Had to watch some of these videos on VLC, flip the image horizontally. My god! Nancy is drop dead gorgeous.

• Can you use trig sub to differentiate?

• I Lost my concentration. Why??

• your videos help so much! can you make a video on Application of integration to Arc Length and area, approximate integration and improper integrals?? Thank you so much for all you do!

• I love math, and I’ll have all of this down pretty soon. But at first exposure… it’s kind of insane how wild solving these problems is getting lol

• mam can you please make a vedio of method of substitution!!!!please mam

• I don’t understand how square root of 36-x^2 changes into 6cos of theta, can someone explain

• Nice

• Can you explain me
How can we decided..what can be considered as ‘ t ‘ out of numerator or dinominator in case of integration by substitution method of integration

• This is the most random recommend video I’ve ever gotten. I haven’t had to do this since freshman year and I don’t plan on doing it this year or my senior year.

• Any idea where we can find some practice problems?

• This really helped my out on my test. Thanks Megan Fox, very cool!

• i heard to replay 7:51 like 20 times and the closed captions confirmed it.

• “This is, a bit of a clusterfuck. This is more than you would ever ask for.” THANK YOU! SOMEONE SAID IT!

• You should do more

• I feel like my tuition money would go to better use to you than my math teacher.

• 0:38 when you fall in love with your student which he is actually a cool guy in class

• Terrible.

• I dont understand at all.
Poor me.😕

• Lmaoooo

• Will you ever do partial fractions?

• Isn’t it suppose to be 125/8 not 125/4?

• I wonder if she realizes how pretty she is.

• you are a life saver for me. Thanks a lot 🙂

• Dude is it just me or is it impressive she can write in mirror reverse. Seriously though channels like yours make math seem simple for everyone 😀

• You do realize people don’t actually do that right?, Its pretty obvious considering you’re smart enough to learn integration.

• Like ur top or what it’s called

• Wish me best of luck guys. It’s midnight now & tomorrow is my exam. But here I am binge watching her tutorials which are not related to my exam topics at all.

• I was struggling with this section. Thanks

• “I know I love finding new integration techniques in my free time” giiiiirl in need that brain ♥️

• Pls post a video proving that the trig substitution gets the right answer.

• 1+1=2 lol

• c l u s t e r f u c k

• Is she left or right handed?

• 20:49 how to integrate that?

• u-sub then power rule

• NancyPi notice me crush,plss

• thanks nancy!

• “replace those x’s and clean it up” hmmmmmmm

• The integral of cluster fuck is

fuck yeah.

• you make me want to watch math videos

• Pause at 7:52 and her look sums trig sub up pretty well 🙂

• I don’t even have maths as a subject…but im interested now 😁

• I skip this shit in the exam

• Hi I love you
Will you marry me I am 18years old

• Teacher Nancy could you make a video without appearing on it ? Because all the video I was focusing on you instead of the explanation , you are so cute !!

• clusterfug?

• Nancy you are looking cool in this dress

• you are great woman i salute you. thanks for all your videos

• sugar britches what can we do with this

• “Don’t worry! I’ll be right by your side.” Awww, Nancy!

• Come to India,………….

• Need more example

• @1:50 Nancy compliments your intelligence!!!!

• There _has to be a better way to get sardines out of a can

• My god your so attractive. Wtf. Stop it just stop it already your killin me over here.🤔🤔🌹🌹🌹

• wait, is her writing backwards???

• I will like private lessons when i am alone at home…

• Sure, private online

• I feel lost knowing that this is as far as Nancy takes us into calculus 😭 thank you Nancy!

• Love watching her videos, whatever it is she’s trying to explain I don’t understand. It just makes me concentrate more on delivery

• at 17:40 wouldn’t the sqrt[(2tantheta)^2+4] be equal to sqrt[(2tantheta)^2+2]? I don’t understand how she got what she had there.

• @7:50 when you’re not used to Nancy cursing D:

• Very informative but Closed Caption action wrote cluster-f… lol

• why dont u just draw a triangle and make your life easier

• Thanks Good

• Beautiful and gorgeous Nancy.

• Can I have your contact plz

• Awesome video Nancy! Way to send it on trig substitution. I am cruising through Calc II thanks to your videos. Keep up the great work!

• I fall in love

• It’s a really awesome …..thank you Nancy

• I wish my calculus professor was that gorgeous
my teacher looked like a homeless santa claus…
and he was not very jolly around midterms and the final exam

• I have another Method for integration{( x^2)/ root(a^2-x^2)}dx
We can subsitude sin(u)a=root(a^2-x^2)

• You will left with(cosu) ^2

• Awesome tutorial. She just explains what it is. Where were videos like this when I was a math student? Why didn’t my professors just explain it this simply?

• so I started saying words like *trig-sub* , *u-sub* , guess who’s the coolest guy in the school now

• was searching for this top like hell thnx alot ma’am

• Hello, I am having trouble understanding how she got (cos θ) / (sin^4 θ) 20:45
Could someone explain it please?  😥

• u = sinΦ
you will then use the power rule to help integrate
1/u^4

• MR YUP Thanks! 😁

• Can you make a video on How to to add numbers?

• Thanks

• bless ur soul

• Wow. Ur my idol. You just saved me for my midterm. Greatly appreciate it.

• Ma’am lovve you

• 😮😔

• have you thought about how many engineers you’ve molded?

• I gave up around 7:21 maybe math is a 2-semester course.

• She rights in mirror but still have a better handwriting than me

• 11:30 To solve for cosine why can’t we just divide both sides by 6 and get the same answer we got using the right triangle trick?

• i love you

• Got damn, there’s sooo many steps that you get lost along the way arrrrgghhh. I gotta practice some more because I felt like I got left behind since from the jump.

• You are great mam

• She’s smiling a lot.
She might have met someone….

Just saying

• Me gusta como explica, pero me perdí en su mirada

• Would you like to have my children? Nancy, you need to do more challenging problems.

• How the hell do you ace calculus 2 when it’s this hard?

• It helps so much. Thank u Nancy 💓

• All of a sudden I have an overpowering urge to watch math videos! Please marry me 💐💐🥰🥰

• Not that easy.

• I think imma just do engineering at university so that I have an excuse to assume sin(x) = x every time

• How did we know dx is 6 cos theta d theta at 6:46 please?

• Are u phd??? :))) Marry me plzzzzzzzzzzzz

• aai am luukeeng phor braeed

• Thank you 🙂

• never expected her to curse but okayyy professor. You naughty naughty!!!!!!

• We maza unajua sio poa🤕🤔

• Could u mind clearing my doubt:-
My question is at the time stance 24:30,how did 64|tan|cube turn into tan square theta??