Trick for Memorizing Trig Integrals

[@TubeYou5046s]

A good way to remember the integral of sinu = -cosu + c is just remember the list: Sin Cos -Sin -Cos Then integration is up the list, and differentiation is down the list, and the list loops. Kinda hard to explain, but for example, the differential of sin is cos, and the differential of cos is -Sin. Then the differential of -Sin is -Cos, and the differential of that is Sin again, and so on. Then integration is the same, but reversed 'up' the list.

[@ColesWorldofMathematics]

That's awesome!!!!

[@akinwole]

TutorialsNshiz God bless you... thank you so much... you just saved me from making common mistakes... I won't mind if we become friends [phone]

[@fathimaashara6517]

I was looking for this. It helped me a lot.

[@Ni999]

Very good. Consider writing them on the x-y axis labels, cos is x, sin is y, positive and negative go exactly where you expect. Differentiate clockwise, integrate counterclockwise.

[@ColesWorldofMathematics]

Very nice!👍🏻

[@v6dynamiic895]

For 8 weeks, I struggled with these and you just made everything make sense in 7 minutes!!! Thank you so much, you are a lifesaver!!!!

[@ColesWorldofMathematics]

Glad it helped!

[@aryansingh3642]

2 years back saw ur same video. Just here to thank u as i still haven't forgot what u taught.

[@ColesWorldofMathematics]

Welcome back! That’s awesome that you haven’t forgot! Thanks for sharing!

[@KIKOMOON]

what a life saver!!! this was so clear and straight forward to help memorize a concept that makes no sense to most students. Once you understand the pattern, it literally takes 30 seconds. Whoever complained about the video length being 7min clearly don’t have the patience to understand and learn a tool that might help them pass

[@ColesWorldofMathematics]

Thanks for watching! 👍🏻👍🏻👍🏻 Please share with your friends!

[@Rimedane]

A trick for sin to cos I like to say is "The Merry-Go-Round" because it goes sin -> -cos -> -sin -> cos -> sin. Because if you go far enough into Integration, it goes right back to where it started. Similar to e^x.

[@ColesWorldofMathematics]

Nice trick! Thanks for sharing.

[@jonathoncliffbailey]

Calculus midterm tomorrow on integration by parts, trigonometric integrals, trigonometric substitution, integration of rational functions by partial functions, and improper integration. D: If it wasn't for videos like this then the master of procrastination would not be able to achieve such a feat. Great video. Instantly memorized! Now on to the hard stuff. :D

[@ColesWorldofMathematics]

Loved your comment!!!!! Good luck tomorrow!

[@FloraSora]

JonBaileyMusic Thanks for the list! I have a test on all of that this Thursday! (It's Sunday Evening)

[@dvaVivy]

How’d you end up in the midterm without memorizing the formulas on the other tests(assumption).

[@sameerroshan9542]

I have the exact same midterm with couple more sections this monday!

[@ColesWorldofMathematics]

Good luck!👍🏻

[@laurencockerspaniel4963]

I was completely hopeless about memorizing these and you made it so easy! My teacher didn't so anything like this to help us, not even separating them into those helpful groups for us! Youre a lifesaver!!!!

[@ColesWorldofMathematics]

So glad this method was helpful for you! Thanks for watching.

[@manishkota4145]

Who else is here the night before the test? Lets be real now

[@marlonarancibia3247]

Morning before

[@Pravein02]

before 3 hours

[@mr.tuttles8288]

Morning before final

[@davispangle9688]

30 minutes before AP test

[@Void_zxiv]

3hours before my term exam😂

[@Malaikas_creation1214]

It'a Malaika here from Pakistan....i saw many videos on integration but never solved my porblem..Thankyou so much ma'am u made it very easy to memorize me these formulas..amazing work..May God bless you with good health...plz pray for me..on 2nd March there is my Maths exam

[@ColesWorldofMathematics]

Glad to hear that. Best of luck to you.

[@erichcurtis79]

you just saved a CAL 2 course

[@ColesWorldofMathematics]

Glad to hear it!

[@connor4531]

The way I remember the anti-derivatives and derivatives of sin or cos is through a level system. If you imagine integration as going up a level and differentiation as going down a level then you just need to remember this: -c s c -s where for derivatives -cosx derives to sinx, sinx derives to cosx, cosx derives to -sinx and then it loops to -sinx derives to -cosx and vice versa for integrals. This is what I was taught by my maths teacher and it helped me out a lot, it's second nature now. When drawing the four letters I say in my head "C, S, C, S - Negatives at the ends"

[@ColesWorldofMathematics]

Thanks! I have had one other person tell me the same trick. It's definitely a good way to remember the derivatives and integrals for sin and cos.

[@patrickmayer9218]

Thank you for making sense of this madness! I'm glad people like you have found ways to make this easy to understand!

[@ColesWorldofMathematics]

Glad to help!

[@SalAlhammadi]

The world need more teachers like you, your explanation are incredibly clear and straight to the point. Thank you from the bottom of my heart

[@ColesWorldofMathematics]

Thank you so much! So glad my videos are helpful!

[@Mike-ks6qu]

The only thing holding me back in calc 1 and 2 was this. Wow this helps so much. It's all fun and games on your exam until you see trig functions...

[@ColesWorldofMathematics]

lol.....glad this helped! Trig functions seem to be a nightmare for a lot of people!

[@u2s5thmember]

Amazing! "PSST" shows up in any page of my trig derivative calculations and now it will make integrating them a breeze too. You are truly amazing. Thanks so much for seeing this trend (or at least posting it)!

[@ColesWorldofMathematics]

You're welcome! So glad it was helpful for you! Please share with your friends.

[@Padthai_Shrimp]

Someone please many copies of these videos, they must be preserved!!!!

[@Bukaloom]

Thank you so much, Cole. I'm taking Calculus II at CCNY and this helps tremendously.

[@ColesWorldofMathematics]

So very glad the video was helpful! Good luck with your course! Thanks for watching.

[@abder4980]

this is so crazy im here 5 years later, studying for Calculus II at CCNY

[@success9271]

@@abder4980 Calc at CCNY is no joke. If you're already on a video like this, you're doing something right, so I am confident you will do great. I wish you the best. Godspeed trooper.

[@TamTran-uo6fz]

Bless your soul, for making a concept so understandable in 7 minutes. I am very grateful for your content.

[@ColesWorldofMathematics]

So glad the videos are helpful for you!

[@sagacioussam5462]

This is all I've ever needed, a good old integration trick that eases the burden on my low functioning brain. I feel you should upload more frequently. Thanks heaps for this one! Greetings from New Delhi!

[@ColesWorldofMathematics]

Thanks! I wish I could upload more frequently. I teach full time at my local high school and part time at a nearby university, so my free time to make videos is limited. Starting in January, I will try to do at least 1 new video a week.

[@andreyshor1743]

YOU ARE LITERALLY AMAZING! YOU SAVED ME ABOUT 3 HRS OF SLEEP! THANK YOU SO MUCH :)))))

[@ColesWorldofMathematics]

Thanks! So glad the video helped you out. Thanks for watching.

[@wahidajannat6376]

Omg!!! I HAVE LEARNED EVERYTHING IN 5 mins, WHAT I HAVE BEEN TRYING TO MEMORIZE/LEARN FOR LAST TWO MONTHS!!!

[@ColesWorldofMathematics]

So glad the video was helpful for you! Please share with your friends so they can benefit too! Thanks.

[@govind8300]

Thanks a lot.Keep Posting. I'm grateful that I found your channel.

[@ColesWorldofMathematics]

You bet! Thanks for watching.

[@jackbalitok3910]

I'm amazed, every lazy student should watch this :) Thank you ma'am.

[@ColesWorldofMathematics]

You're welcome! Anything to make it easier!

[@redeem5]

Thank you for this video! This was actually very helpful and I wish I would've found this information last semester because this is the easiest way I've seen to memorize these integrals.

[@ColesWorldofMathematics]

Glad it helped you!

[@kevin15664]

I'm a Jr.level ME student taking ODE and this just saved my hide. I remember one thing in cal 2 and that is that it sucked. Hard. Thank you Prof!

[@ColesWorldofMathematics]

Glad it helped!

[@mavisuy9520]

I just memorized this for just less than 10 minutes. Thank you so much!

[@ColesWorldofMathematics]

+Mavis Uy Glad it helped!

[@omarpalacios9734]

Oh my goodness!! So splendid how to memorize the Double function integrals!!!! Way to go ! Thanks a lot, you have just saved my life! :

[@ColesWorldofMathematics]

Glad it helped you!

[@subby_tech]

Thank you very much! This video made it much easier to memorize the integrals of the trig functions!

[@ColesWorldofMathematics]

+Subby Ramesh You're Welcome! Glad the video was able to help!

[@catchingchair]

I have a Calc Exam Tomorrow and this saved me. Thank you so much!

[@ColesWorldofMathematics]

Best of luck!

[@Marcus001]

7 years on this is still saving grades

[@ColesWorldofMathematics]

So true!

[@kaushikbarman1658]

Heartiest like I have ever dropped on any KZbin video.

[@ColesWorldofMathematics]

That’s awesome! Thanks for sharing!

[@mikemendrala1781]

I don’t understand why this isn’t the way it is taught. Thanks so much 🙏

[@ColesWorldofMathematics]

Thanks.

[@sydneyelizabeth1343]

Thank you for such helpful videos! I don't know how I could make it through Calculus without youtubers like you!

[@ColesWorldofMathematics]

You're welcome! Glad it helped! Thanks for watching!

[@McMo64]

Great job explaining these equations! This will definitely help me remember with all these cool tricks you have.

[@ColesWorldofMathematics]

Very glad the video was helpful for you! Thanks for watching. Please share with your friends.

[@skeletonclip]

just got a math's exam next week and this saved my life, very helpful by the way.

[@ColesWorldofMathematics]

Great to hear!

[@tycobrahe7663]

(Lumping together+pattern recognition): brilliant! Made it soooo easy to remember!

[@Akshayyy554]

I just wanna thankyou with the bottom of my heart 🌌🙏

[@skye-chor]

omg... you're literally a life saver

[@ColesWorldofMathematics]

Thanks so much.

[@emiraniba9624]

THE MOST INCREDIBLE TRICK IVE EVER SEEN.

[@ColesWorldofMathematics]

Thanks! 👍🏻

[@Farrukhw]

Waooo, that's so easy, never thought of that... What a way to teach... Thanks a bunch :)...

[@ColesWorldofMathematics]

You're welcome! So glad the technique was helpful for you! Thanks for watching. Please share with your friends so others can benefit too. 👍😃

[@andrewandrew2791]

you are the GOAT, thanks a lot this helped me in calculus and calculus 2!!

[@ColesWorldofMathematics]

Thanks so much! Glad it helped you out!

[@lukefranzen6670]

That table at the top left is so useful thank you

[@ColesWorldofMathematics]

You’re welcome 😊

[@leigh835]

About to take my final tomorrow and this method is absolutely amazing. Thank you so much!!

[@ColesWorldofMathematics]

I hope you did well on your final!👍

[@ducksoop.x]

Calc I was such a breeze, I'm taking Calc II right now and it sure has been exponentially more difficult. But this is a lifesaver right here!

[@ColesWorldofMathematics]

Great! So glad it's helpful for you! Good luck in Calc II.

[@ThePiMan0903]

Thanks for your video Cole. I find your videos really helpful. Subscribed

[@ColesWorldofMathematics]

I'm slow to reply.....but definitely thanks!

[@billwindsor4224]

Excellent video on a framework for memorizing trig integrals; thank you!

[@ColesWorldofMathematics]

Thank you for the nice comments! I appreciate it!

[@alexchen5156]

Hi, your videos are very helpful, thanks! But one question: the intergral of tan is LN |sec u| + C, how come you wrote it as - ln |cos u| +c

[@ColesWorldofMathematics]

Actually, both your answer and my answer are equivalent. Check this link out to see the algebra steps to verify it: www.dropbox.com/s/xr56g0wvul64zr9/Integral%20Tan.pdf?dl=0

[@alexchen5156]

Got it, thanks a lot!

[@nicholasbaluku1496]

Wows , Thanks alot, You make it very simple and easy. Iam impressed and you have helped me and boosted my confidence. Please make more videos for all the other mathematics Topics.

[@ColesWorldofMathematics]

So glad the videos are helpful! Since August, I have been focusing on Calculus videos, but I can start to make more of a variety of different topics. Be sure to check out all my various playlists: kzbin.info/door/Kl7MXLRrk6hnWuObFwKxdgplaylists?disable_polymer=1

[@saira18926]

oh my gosh you are a gift to humanity. thanks so much!

[@ColesWorldofMathematics]

Thanks! Glad you are finding the videos helpful!

[@Rhombus-inc]

i have a calc 3 exam tomorrow and its 11:29 pm this video really helped fr me to atlaest understand the basics 😀❤❤

[@ColesWorldofMathematics]

Best of luck on your exam.

[@shashankravi478]

Great video.. Thanks. Feels so easy to remember such stuffs now on. Please make more of such videos. Thank you once again!!

[@ColesWorldofMathematics]

Will do! Thanks for watching!

[@Capsula_tm]

you made my life easier thank youuu!!!!!

[@ColesWorldofMathematics]

Happy to help!

[@MunisaR]

I have calc exam on these topics(tomorrow) ...from chapter 4~7. God save me. Your video helped me so much. I was struggling how to memorize these formulas. Thankkkk uuuuu

[@ColesWorldofMathematics]

So glad my videos have been helpful! Thanks for watching.

[@rachel145]

you’re doing god’s work

[@ColesWorldofMathematics]

Thanks!

[@1187624]

The greatest trick of all time!!

[@ColesWorldofMathematics]

Yep! ❤️👍🏻

[@Don_XI]

thank you for sharing your knowledge with us

[@ColesWorldofMathematics]

My pleasure!

[@mylobage]

If I could like this more I would. No lie. At least 50 more times. This is a beautiful table for memorization.

[@ColesWorldofMathematics]

Thank you so much. I can’t take credit for creating it, but explaining it well and implementing it correctly makes all the difference in the world! Thanks for watching!

[@SubalaPeriyasamy]

Keep up the great vids! This really helped me, when i studied the sunday before the exams😅

[@ColesWorldofMathematics]

Glad I could help!

[@pavitraravishankar2293]

This video is just amaaaazziiinnnggg❤️❤️❤️. I can't believe I learnt it this quick😀. You are just awesome 💫.

[@ColesWorldofMathematics]

Thank you so much! Thanks for watching. Please share with your friends.

[@Luingus]

for the sec sec tan square you pick one and choose two for derivatives and pick two and choose one for integrals.

[@LoVeMyWiShEs]

youre a magician, this is amazing

[@ColesWorldofMathematics]

Thanks, greatly appreciated.

[@a4rules2]

YOU ATE this might save me on my calc test in 15 minutes 😍

[@ColesWorldofMathematics]

😋

[@johnjose6397]

U r one hell of a genius

[@ColesWorldofMathematics]

👍

[@shahbaztariq2837]

Thats Brilliant! Thanks a ton ❤️

[@Debonairfox]

Very informative and helpful. You did such a great job with this video!

[@ColesWorldofMathematics]

+Debonair Fox Thanks! Memorizing Trig Integrals can be difficult for students so knowing some tricks can be helpful!

[@Debonairfox]

Yeah definitely. If you have any other tips would love to hear them. Will be looking forward to more of your videos and perhaps even catching you in our comments sometime :)

[@SuperGirlygirl222]

Thank you so much! this saves a lot of time and i can easily compute any of them right away!

[@ColesWorldofMathematics]

You are welcome! So glad it helped!

[@jennyl.8170]

We love you!!! You're a genius and a saint!!

[@ColesWorldofMathematics]

Thanks!

[@dougjenkins7311]

THIS IS AWESOME!!!!!!!! THANK YOU SO MUCH!!!!! Please make more videos like this.

[@ColesWorldofMathematics]

You're welcome! I will do my best to make more like this one.

[@alishshrsetha1290]

Thank you very very very much. It was very very very help full.

[@ColesWorldofMathematics]

+alish shrsetha You're welcome! Glad it helped!!!!

[@blahhhhidk]

this is the most helpful video ive watched for calc today tysm!!

[@ColesWorldofMathematics]

So glad the video was helpful for you! Please share with your friends.

[@lanasalah704]

You are such a genius👍👍👍

[@ColesWorldofMathematics]

Thanks! :-)

[@maplekyle8577]

I am glad I found this video before my test. Smart Memory! Thxxxxx

[@ColesWorldofMathematics]

Hope you did well! Check back for more helpful Calculus videos!

[@AliRaza_s_Ai]

You just saved my today's quiz thanks a lot mam

[@ColesWorldofMathematics]

Glad to hear that! Good luck!

[@tasfiatabassum5130]

thank you so much, it really helped me memorize them :) i appreciate your effort

[@ColesWorldofMathematics]

Anytime! I enjoy making videos and helping people with math!

[@AliHassan-hb1bn]

I loved your lectures girl, only God can reward you

[@ColesWorldofMathematics]

Thank you so much! 🙂

[@arjundulam6354]

Great video to prep for AP Calc exam!

[@ColesWorldofMathematics]

Glad it was helpful!

[@JannahMa-n7u]

so glad i found this video. will gatekeep .

[@ColesWorldofMathematics]

Awesome! Enjoy!

[@nandakumar8060]

Thankyou very much......u saved me from calculus😭😭😭

[@ColesWorldofMathematics]

You're welcome! Thanks for watching. Glad it was helpful!

[@bafanamthembu384]

Wow lady u just made maths easy very easy

[@ColesWorldofMathematics]

Thanks! Glad it helped!

[@168grhp]

Extremely helpful! Thank you for sharing!

[@ColesWorldofMathematics]

You're welcome! Thanks for watching!

[@sofilovestea]

thank you, thank you! greetings from Costa Rica

[@ColesWorldofMathematics]

You're welcome!

[@phy-sink3081]

madam you are all right but when you takes the integral of tan is not right at atol..and the integral of tan is written as.{tanu.du=ln(secu)+c

[@ColesWorldofMathematics]

You are correct. However, I am too. The answer I gave in the video and your answer are equivalent answers. The integral of tan(u) du = - ln|cos u| + c ==> ln| (cos u)^-1 | + c ==> ln| 1/cos u | + c ==> ln|sec u| + c

[@maharanirani54]

Thank you! This is super helpful!

[@ColesWorldofMathematics]

Glad it was helpful! Thanks for watching & commenting.

[@Yelouboiee]

English: I love you. Spanish: Te amo. French: Je t'aime. German: Ich liebe dich. Italian: Ti amo. Portuguese: Eu te amo. Dutch: Ik hou van je. Russian: Ya tebya lyublyu. Chinese (Mandarin): Wă ài ni Japanese: Ai shiteru. Korean: Saranghaeyo. Arabic: Uhibbuka. Turkish: Seni seviyorum. Greek: Se agapó. Hindi: Main tumsepyaar karta/karti hoon. Swedish: Jag älskar dig. Norwegian: Jeg elsker deg. Danish: Jeg elsker dig. Finnish: Rakastan sinua. Polish: Kocham cię. Czech: Miluji tě. Hungarian: Szeretlek. Czech: Miluji tě. Romanian: Te iubesc. Bulgarian: Obicham te. Ukrainian: Ya tebe kokhayu. Hebrew: Ani ohev otakh/otkha. Indonesian: Aku cinta kamu. Vietnamese: Anh yêu em (Male to female), Em yêu anh (Female to male). Thai: Chan rak ter. Filipino: Mahal kita. Malay: Saya cintakan awak. Swahili: Nakupenda Afrikaans: Ek het jou lief Catalan: T'estimo. Estonian: Ma armastan sind. Lithuanian: Aš tave myliu Latvian: Es tevi milu. Slovak: Milujem ta. Slovenian: Ljubim te. Albanian: Te dua. Macedonian: Te sakam. Serbian: Volim te. Croatian: Volim te. Bosnian: Volim te. Icelandic: Ég elska þig. Welsh: Rwy'n dy garu di. lrish: Tá grá agam duit. Scottish Gaelic: Tha gaol agam ort. Basque: Maite zaitut. Corsican: Ti tengu caru Maltese: Inhobbok. Yiddish: Ikh hob dir lib. Luxembourgish: Ech hunn dech gär. Malagasy: Tiako ianao. Hausa: Ina sonka. Igbo: Achorom gi n'anya. Somali: Waan ku jeclahay. Zulu: Ngiyakuthanda Xhosa: Ndiyakuthanda. Sesotho: Ke a o rata. Esperanto: Mi amas vin. Javanese: Aku tresno awakmu Bengali: Ami tomai bhalobashi. Gujarati: Hum tane prêma karum chum. Kannada: Nanu ninnannu prītisuttēne. Malayalam: Njān ninne snehikkunnu. Marathi: Majham tumhālā prēma karatõ. Nepali: Ma timila'i māyā garchhu. Odia: Mum tumaku bhalapa'im. Punjabi: Main tain piyar karadā hầm. Sindhi: Man twan ji mahabbat kiyandī. Tamil: Nān unnai kātalikkirēn. Telugu: Nanu ninnu prēmistunnānu. Urdu: Main tum se pyaar karta/karti hoon. Uzbek: Seni sevaman Kazakh: Seni süyemin. Kyrgyz: Seni süyöm. Tajik: Man toro dūst medoram. Turkmen: Men seni söýärin. Georgian: Miqvarxar. Armenian: Yes kez sirum em. Azeri: Mən səni sevirəm. Amharic: Ewedeshalehu. Hausa: Ina sonka. Kurdish: Ez te hezdikhem, Pashto: Za te dost kum. Sinhala: Mama oyata ādarēyi. Sundanese: Abdi cinta ka anjeun Uzbek: Men sizni sevaman. Uighur: Men sizni yaxshi ko'remen. Filipino: Iniibig kita. Hawaiian: Aloha au ia 'oe. Maori: Aroha ana ahau ki a koe. Samoan: Ou te alofa ia te oe. Tahitian: Ua here au ia oe. Fijian: Au lomani iko. Maori: E aroha ana ahau ki a koe. Tongan: 'Ofa 'atu kihe koe. Marshallese: Jekwe en in jeik. Pidgin English: Mi lusim yu. Dzongkha:Nga choe lu ga

[@pranashaktiyog]

Your tricks are just awesome!! 😍

[@ColesWorldofMathematics]

Thanks!

[@quenieromorosa5957]

This technique is helpful. Thanks a lot!

[@ColesWorldofMathematics]

Glad it was helpful. Thanks for watching and commenting.

[@starshipx1282]

Immediately subscribed.

[@ColesWorldofMathematics]

Awesome! Thanks.

[@gbrlgd]

OH MY GOD THANK YOU VERY MUCH!

[@ColesWorldofMathematics]

You're welcome! Thanks for watching!

[@zeno802]

Hey can you please tell me how can i memorize the trigonometric identities. For eg- 1-cos2x = 2(sin^2)x Im having a hell lot of problems in those.

[@joeycarlyle1949]

THANK YOU SO MUCH! WHY CAN'T MY TEACHER TEACH US THIS WAY

[@shin-ishikiri-no]

Why is the second "double function" integral not following the guide according to the chart...? Shouldn't the answer be [cot(u) du + c] instead of [-cot(u) du + c]...? How did you magic grab that negative?

[@ColesWorldofMathematics]

The answer to the second "double function" is [-cot(u) +c] because looking at the bottom row of the chart, you have 2 csc's, a negative sign, and cot. The integral of csc^2 uses the 2 csc's, so your answer is everything that is left in the bottom row of the chart. Thus, [-cot(u)+c].

[@MOHAMMEDSOHAILalzwjAyesha]

Awesome sir , really very use full and decreased load on my Brian

[@ColesWorldofMathematics]

Great to hear!

[@inderdeepk.dhanoa2788]

Thankyou so much.. I have been Mugging up these formulae since last 2 years :D ♡

[@ColesWorldofMathematics]

You're welcome! Glad it was helpful!

[@noumanhaider4893]

Not only liked your video patients of calculus loved it.....!

[@ColesWorldofMathematics]

Super big thank! 👍🏻😃

[@jamesd9215]

All i ever needed. Thank you so much

[@ColesWorldofMathematics]

You're welcome! Thanks for watching!

[@laithal-kinani2249]

You, good sir, are a legend

[@ColesWorldofMathematics]

Thanks!

[@hemanthreddie]

Got ready for the exam tomorrow THANK YOU !!!!!!! 😊😊😊😊😊😊😊😊😊😊😊😊😊😊

[@ColesWorldofMathematics]

You're welcome! Hope the exam went well!!!!

[@getachewadem9160]

you got good????

[@bemnetbayih1210]

U so more than smart , love ur video

[@hammuhamju5320]

Thank you so much mam,GOD bless you

[@ColesWorldofMathematics]

You are most welcome! All the best to you!