Trick for Memorizing Trig Integrals
Рет қаралды 358,457
Күн бұрынThis video describes a method for helping students to memorize the Basic Trig Integrals.
For the Integral of Tan, - ln |cos u| + c and ln|sec u| + c are equivalent answers. To see the algebraic verification, follow this link:
bit.ly/2pBn5wE
#mathematics #calculus #trigintegrals
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For clarification, I did not create this mnemonic device for remembering trig integrals. Variations of this mnemonic device can be found all around the internet. For example, Tim Pettis presents a similar method in a Prezi Presentation, Mark Ryan presents a similar method in his book "Calculus Essentials for Dummies", MalignedAnus describes the method in a post on Reddit, and Vedant Mehta has created a KZfaq video.
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@v6dynamiic895 2 жыл бұрын
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 2 жыл бұрын
Glad it helped!
@aryansingh3642 Жыл бұрын
2 years back saw ur same video. Just here to thank u as i still haven't forgot what u taught.
@ColesWorldofMathematics Жыл бұрын
Welcome back! That’s awesome that you haven’t forgot! Thanks for sharing!
@erichcurtis79 7 жыл бұрын
you just saved a CAL 2 course
@ColesWorldofMathematics 7 жыл бұрын
Glad to hear it!
@TubeYou5046s 7 жыл бұрын
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 7 жыл бұрын
That's awesome!!!!
@akinwole 5 жыл бұрын
TutorialsNshiz God bless you... thank you so much... you just saved me from making common mistakes... I won't mind if we become friends +2348104795824
@fathimaashara6517 5 жыл бұрын
I was looking for this. It helped me a lot.
@Ni999 5 жыл бұрын
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 5 жыл бұрын
Very nice!👍🏻
@KIKOMOON 4 жыл бұрын
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 4 жыл бұрын
Thanks for watching! 👍🏻👍🏻👍🏻 Please share with your friends!
@laurencockerspaniel4963 6 жыл бұрын
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 6 жыл бұрын
So glad this method was helpful for you! Thanks for watching.
@patrickmayer9218 2 жыл бұрын
Thank you for making sense of this madness! I'm glad people like you have found ways to make this easy to understand!
@ColesWorldofMathematics 2 жыл бұрын
Glad to help!
@jonathoncliffbailey 7 жыл бұрын
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 7 жыл бұрын
Loved your comment!!!!! Good luck tomorrow!
@FloraSora 7 жыл бұрын
JonBaileyMusic Thanks for the list! I have a test on all of that this Thursday! (It's Sunday Evening)
@dvaVivy 5 жыл бұрын
How’d you end up in the midterm without memorizing the formulas on the other tests(assumption).
@sameerroshan9542 5 жыл бұрын
I have the exact same midterm with couple more sections this monday!
@ColesWorldofMathematics 5 жыл бұрын
Good luck!👍🏻
@redeem5 7 жыл бұрын
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 7 жыл бұрын
Glad it helped you!
@TamTran-uo6fz 2 жыл бұрын
Bless your soul, for making a concept so understandable in 7 minutes. I am very grateful for your content.
@ColesWorldofMathematics 2 жыл бұрын
So glad the videos are helpful for you!
@Padthai_Shrimp 3 жыл бұрын
Someone please many copies of these videos, they must be preserved!!!!
@McMo64 5 жыл бұрын
Great job explaining these equations! This will definitely help me remember with all these cool tricks you have.
@ColesWorldofMathematics 5 жыл бұрын
Very glad the video was helpful for you! Thanks for watching. Please share with your friends.
@u2s5thmember 6 жыл бұрын
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 6 жыл бұрын
You're welcome! So glad it was helpful for you! Please share with your friends.
@manishkota4145 3 жыл бұрын
Who else is here the night before the test? Lets be real now
@marlonarancibia3247 2 ай бұрын
Morning before
@Yuki_dxdy 2 ай бұрын
before 3 hours
@mr.tuttles8288 2 ай бұрын
Morning before final
@davispangle9688 Ай бұрын
30 minutes before AP test
@subby_tech 8 жыл бұрын
Thank you very much! This video made it much easier to memorize the integrals of the trig functions!
@ColesWorldofMathematics 8 жыл бұрын
+Subby Ramesh You're Welcome! Glad the video was able to help!
@Malaikas_creation1214 2 ай бұрын
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 2 ай бұрын
Glad to hear that. Best of luck to you.
@govind8300 6 жыл бұрын
Thanks a lot.Keep Posting. I'm grateful that I found your channel.
@ColesWorldofMathematics 6 жыл бұрын
You bet! Thanks for watching.
@sydneyelizabeth1343 7 жыл бұрын
Thank you for such helpful videos! I don't know how I could make it through Calculus without youtubers like you!
@ColesWorldofMathematics 7 жыл бұрын
You're welcome! Glad it helped! Thanks for watching!
@jackbalitok3910 8 жыл бұрын
I'm amazed, every lazy student should watch this :) Thank you ma'am.
@ColesWorldofMathematics 7 жыл бұрын
You're welcome! Anything to make it easier!
@Bukaloom 6 жыл бұрын
Thank you so much, Cole. I'm taking Calculus II at CCNY and this helps tremendously.
@ColesWorldofMathematics 6 жыл бұрын
So very glad the video was helpful! Good luck with your course! Thanks for watching.
@abder4980 9 ай бұрын
this is so crazy im here 5 years later, studying for Calculus II at CCNY
@success9271 7 ай бұрын
@@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.
@tycobrahe7663 4 жыл бұрын
(Lumping together+pattern recognition): brilliant! Made it soooo easy to remember!
@Mike-ks6qu 4 жыл бұрын
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 4 жыл бұрын
lol.....glad this helped! Trig functions seem to be a nightmare for a lot of people!
@shahbaztariq2837 Ай бұрын
Thats Brilliant! Thanks a ton ❤️
@shashankravi478 4 жыл бұрын
Great video.. Thanks. Feels so easy to remember such stuffs now on. Please make more of such videos. Thank you once again!!
@ColesWorldofMathematics 4 жыл бұрын
Will do! Thanks for watching!
@billwindsor4224 7 жыл бұрын
Excellent video on a framework for memorizing trig integrals; thank you!
@ColesWorldofMathematics 7 жыл бұрын
Thank you for the nice comments! I appreciate it!
@tasfiatabassum5130 8 жыл бұрын
thank you so much, it really helped me memorize them :) i appreciate your effort
@ColesWorldofMathematics 8 жыл бұрын
Anytime! I enjoy making videos and helping people with math!
@leigh835 Жыл бұрын
About to take my final tomorrow and this method is absolutely amazing. Thank you so much!!
@ColesWorldofMathematics Жыл бұрын
I hope you did well on your final!👍
@SuperGirlygirl222 7 жыл бұрын
Thank you so much! this saves a lot of time and i can easily compute any of them right away!
@ColesWorldofMathematics 7 жыл бұрын
You are welcome! So glad it helped!
@168grhp 7 жыл бұрын
Extremely helpful! Thank you for sharing!
@ColesWorldofMathematics 7 жыл бұрын
You're welcome! Thanks for watching!
@omarpalacios9734 7 жыл бұрын
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 7 жыл бұрын
Glad it helped you!
@kevin15664 7 жыл бұрын
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 7 жыл бұрын
Glad it helped!
@mavisuy9520 8 жыл бұрын
I just memorized this for just less than 10 minutes. Thank you so much!
@ColesWorldofMathematics 8 жыл бұрын
+Mavis Uy Glad it helped!
@andreyshor1743 6 жыл бұрын
YOU ARE LITERALLY AMAZING! YOU SAVED ME ABOUT 3 HRS OF SLEEP! THANK YOU SO MUCH :)))))
@ColesWorldofMathematics 6 жыл бұрын
Thanks! So glad the video helped you out. Thanks for watching.
@andrewandrew2791 4 ай бұрын
you are the GOAT, thanks a lot this helped me in calculus and calculus 2!!
@ColesWorldofMathematics 4 ай бұрын
Thanks so much! Glad it helped you out!
@dougjenkins7311 7 жыл бұрын
THIS IS AWESOME!!!!!!!! THANK YOU SO MUCH!!!!! Please make more videos like this.
@ColesWorldofMathematics 7 жыл бұрын
You're welcome! I will do my best to make more like this one.
@SalAlhammadi 6 жыл бұрын
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 6 жыл бұрын
Thank you so much! So glad my videos are helpful!
@ThePiMan0903 Жыл бұрын
Thanks for your video Cole. I find your videos really helpful. Subscribed
@ColesWorldofMathematics 8 ай бұрын
I'm slow to reply.....but definitely thanks!
@pavitraravishankar2293 6 жыл бұрын
This video is just amaaaazziiinnnggg❤️❤️❤️. I can't believe I learnt it this quick😀. You are just awesome 💫.
@ColesWorldofMathematics 6 жыл бұрын
Thank you so much! Thanks for watching. Please share with your friends.
@Debonairfox 8 жыл бұрын
Very informative and helpful. You did such a great job with this video!
@ColesWorldofMathematics 8 жыл бұрын
+Debonair Fox Thanks! Memorizing Trig Integrals can be difficult for students so knowing some tricks can be helpful!
@Debonairfox 8 жыл бұрын
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 :)
@Akshayyy554 2 жыл бұрын
I just wanna thankyou with the bottom of my heart 🌌🙏
@catchingchair 2 ай бұрын
I have a Calc Exam Tomorrow and this saved me. Thank you so much!
@ColesWorldofMathematics 2 ай бұрын
Best of luck!
@blahhhhidk 6 жыл бұрын
this is the most helpful video ive watched for calc today tysm!!
@ColesWorldofMathematics 6 жыл бұрын
So glad the video was helpful for you! Please share with your friends.
@sagacioussam5462 7 жыл бұрын
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 7 жыл бұрын
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.
@joeycarlyle1949 7 жыл бұрын
THANK YOU SO MUCH! WHY CAN'T MY TEACHER TEACH US THIS WAY
@inderdeepk.dhanoa2788 7 жыл бұрын
Thankyou so much.. I have been Mugging up these formulae since last 2 years :D ♡
@ColesWorldofMathematics 7 жыл бұрын
You're welcome! Glad it was helpful!
@yousefchaudhary5080 7 жыл бұрын
This was incredibly helpful. Thank you!
@ColesWorldofMathematics 7 жыл бұрын
You're welcome!
@connor4531 7 жыл бұрын
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 7 жыл бұрын
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.
@mikemendrala1781 3 ай бұрын
I don’t understand why this isn’t the way it is taught. Thanks so much 🙏
@ColesWorldofMathematics 3 ай бұрын
Thanks.
@alishshrsetha1290 8 жыл бұрын
Thank you very very very much. It was very very very help full.
@ColesWorldofMathematics 8 жыл бұрын
+alish shrsetha You're welcome! Glad it helped!!!!
@Farrukhw 6 жыл бұрын
Waooo, that's so easy, never thought of that... What a way to teach... Thanks a bunch :)...
@ColesWorldofMathematics 6 жыл бұрын
You're welcome! So glad the technique was helpful for you! Thanks for watching. Please share with your friends so others can benefit too. 👍😃
@maharanirani54 7 ай бұрын
Thank you! This is super helpful!
@ColesWorldofMathematics 7 ай бұрын
Glad it was helpful! Thanks for watching & commenting.
@user-wy9cl1kf2f 3 ай бұрын
Keep up the great vids! This really helped me, when i studied the sunday before the exams😅
@ColesWorldofMathematics 3 ай бұрын
Glad I could help!
@FatimaZahra-lh7ll 4 жыл бұрын
Thank you so much!
@lukefranzen6670 Жыл бұрын
That table at the top left is so useful thank you
@ColesWorldofMathematics Жыл бұрын
You’re welcome 😊
@saira18926 6 жыл бұрын
oh my gosh you are a gift to humanity. thanks so much!
@ColesWorldofMathematics 6 жыл бұрын
Thanks! Glad you are finding the videos helpful!
@wahidajannat6376 6 жыл бұрын
Omg!!! I HAVE LEARNED EVERYTHING IN 5 mins, WHAT I HAVE BEEN TRYING TO MEMORIZE/LEARN FOR LAST TWO MONTHS!!!
@ColesWorldofMathematics 6 жыл бұрын
So glad the video was helpful for you! Please share with your friends so they can benefit too! Thanks.
@maplekyle8577 6 жыл бұрын
I am glad I found this video before my test. Smart Memory! Thxxxxx
@ColesWorldofMathematics 6 жыл бұрын
Hope you did well! Check back for more helpful Calculus videos!
@pistachio66 4 жыл бұрын
Do these work if you replace u with x? If I get a problem that says sec^2 x would the integral would be tan x ?
@nicholasbaluku1496 6 жыл бұрын
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 6 жыл бұрын
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: kzfaq.info/love/Kl7MXLRrk6hnWuObFwKxdgplaylists?disable_polymer=1
@ducksoop.x 6 жыл бұрын
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 6 жыл бұрын
Great! So glad it's helpful for you! Good luck in Calc II.
@ananthanarayananv8490 2 жыл бұрын
thank you very much ! It was a very helpful video to memorize these formulas.
@ColesWorldofMathematics 2 жыл бұрын
Glad it was helpful!
@jamesd9215 7 жыл бұрын
All i ever needed. Thank you so much
@ColesWorldofMathematics 7 жыл бұрын
You're welcome! Thanks for watching!
@skeletonclip 2 ай бұрын
just got a math's exam next week and this saved my life, very helpful by the way.
@ColesWorldofMathematics 2 ай бұрын
Great to hear!
@drsu5638 3 жыл бұрын
This is so helpful, thank you!
@ColesWorldofMathematics 3 жыл бұрын
You're so welcome!
@Capsula_tm 5 ай бұрын
you made my life easier thank youuu!!!!!
@ColesWorldofMathematics 5 ай бұрын
Happy to help!
@zeno802 2 жыл бұрын
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.
@tiptoncommunityschoolcorpo5372 5 жыл бұрын
This is awesome! Thanks so much for sharing.
@ColesWorldofMathematics 5 жыл бұрын
You're welcome! Thanks for commenting & watching.
@dougjenkins7311 7 жыл бұрын
Greatly appreciated! Thank you.
@ColesWorldofMathematics 7 жыл бұрын
You're welcome! Thanks for watching. Please share with your friends.
@LoVeMyWiShEs 6 жыл бұрын
youre a magician, this is amazing
@ColesWorldofMathematics 6 жыл бұрын
Thanks, greatly appreciated.
@swaggyskye 2 жыл бұрын
omg... you're literally a life saver
@ColesWorldofMathematics 2 жыл бұрын
Thanks so much.
@jennyl.8170 6 жыл бұрын
We love you!!! You're a genius and a saint!!
@ColesWorldofMathematics 6 жыл бұрын
Thanks!
@paulkim321 8 жыл бұрын
Thank You so much for this!
@ColesWorldofMathematics 8 жыл бұрын
+Paul Kim You're welcome! Anything to make learning the trig integrals a little easier!
@Luingus 3 жыл бұрын
for the sec sec tan square you pick one and choose two for derivatives and pick two and choose one for integrals.
@pranashaktiyog 6 жыл бұрын
Your tricks are just awesome!! 😍
@ColesWorldofMathematics 6 жыл бұрын
Thanks!
@gbrlgd 7 жыл бұрын
OH MY GOD THANK YOU VERY MUCH!
@ColesWorldofMathematics 7 жыл бұрын
You're welcome! Thanks for watching!
@rajazareef7525 4 жыл бұрын
thank you for sharing this method. it helps a lot!!
@ColesWorldofMathematics 4 жыл бұрын
You’re welcome! Thanks for watching!
@mylobage 5 жыл бұрын
If I could like this more I would. No lie. At least 50 more times. This is a beautiful table for memorization.
@ColesWorldofMathematics 5 жыл бұрын
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!
@emiraniba9624 6 жыл бұрын
THE MOST INCREDIBLE TRICK IVE EVER SEEN.
@ColesWorldofMathematics 6 жыл бұрын
Thanks! 👍🏻
@kaushikbarman1658 5 ай бұрын
Heartiest like I have ever dropped on any KZfaq video.
@ColesWorldofMathematics 4 ай бұрын
That’s awesome! Thanks for sharing!
@quenieromorosa5957 Жыл бұрын
This technique is helpful. Thanks a lot!
@ColesWorldofMathematics Жыл бұрын
Glad it was helpful. Thanks for watching and commenting.
@bemnetbayih1210 4 жыл бұрын
U so more than smart , love ur video
@marissatrujillo487 7 жыл бұрын
So helpful, thank you!!
@ColesWorldofMathematics 7 жыл бұрын
You are welcome! Thanks for watching!
@mandelbrotsugee 5 жыл бұрын
まとめてくれてよかったですね。
@Attamatic 7 жыл бұрын
great video, great effort. May your life be filled with peace and fulfillment
@ColesWorldofMathematics 7 жыл бұрын
Thank you very much for the kind words!
@brydust 6 жыл бұрын
any trick for helping us remember the integral of sec^3(u)? It is a fairly common integrand because of trig substitution
@ColesWorldofMathematics 6 жыл бұрын
Try this: kzfaq.info/get/bejne/m8yhodp9vaqommw.html
@rcfoley 5 жыл бұрын
Very cool, thanks a bunch.
@ColesWorldofMathematics 5 жыл бұрын
You’re welcome! Thanks for watching!
@johnjose6397 5 жыл бұрын
U r one hell of a genius
@ColesWorldofMathematics 5 жыл бұрын
👍
@AtomicPeach 5 жыл бұрын
You're a saint, thank you!
@ColesWorldofMathematics 5 жыл бұрын
Thanks! Thanks for watching.
@junaidmughal3511 3 жыл бұрын
Thank you very much!
@ColesWorldofMathematics 3 жыл бұрын
You're welcome! Thanks for watching.
@sofilovestea 7 жыл бұрын
thank you, thank you! greetings from Costa Rica
@ColesWorldofMathematics 7 жыл бұрын
You're welcome!
@Marcus001 4 ай бұрын
7 years on this is still saving grades
@ColesWorldofMathematics 4 ай бұрын
So true!
@nikhilbanerjee3004 4 жыл бұрын
Youre brilliant!
@ColesWorldofMathematics 4 жыл бұрын
Thanks!
@sirisaacnewton2186 7 жыл бұрын
Thank you soooooo much! This is excellent!!!!!!!
@ColesWorldofMathematics 7 жыл бұрын
Thanks for watching! Please share my channel with your friends!
@BowTie8Bit 5 жыл бұрын
Amazing, thank you!
@ColesWorldofMathematics 5 жыл бұрын
You’re welcome! Thanks for watching! Please share with your friends!
@arjundulam6354 Жыл бұрын
Great video to prep for AP Calc exam!
@ColesWorldofMathematics 11 ай бұрын
Glad it was helpful!
@shri2378 5 жыл бұрын
This is the best video i have ever watched😍mam can u post about triple integration..?
@lanasalah704 7 жыл бұрын
You are such a genius👍👍👍
@ColesWorldofMathematics 7 жыл бұрын
Thanks! :-)
@TheyCallMeD 8 жыл бұрын
Thank you!!!!
@ColesWorldofMathematics 8 жыл бұрын
You're Welcome!!
@sumeetchanda5076 7 жыл бұрын
Thank You so much !! it helped alot..
@ColesWorldofMathematics 7 жыл бұрын
That's great! Thanks for watching!
Cole's World of Mathematics
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