Trigonometric Substitution

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  • Опубликовано: 15 ноя 2024
  • This calculus video tutorial provides a basic introduction into trigonometric substitution. It explains when to substitute x with sin, cos, or sec. It also explains how to perform a change of variables using u-substitution integration techniques and how to use right triangle trigonometry with sohcahtoa to convert back from angles in the form of theta to an x variable. There's plenty of examples and practice problems in this lesson.
    Full 1 Hour 10 Minute Video:
    / mathsciencetutor
    Direct Link to The Full Video:
    www.bit.ly/3zu...
    Integration - Free Formula Sheet:
    bit.ly/3XCT6oz
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    Full 1 Hour 10 Minute Video:
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Комментарии • 480

  • @TheOrganicChemistryTutor
    @TheOrganicChemistryTutor  3 года назад +74

    Integration - Free Formula Sheet: bit.ly/3XCT6oz
    Full 1 Hour 10 Minute Video: www.patreon.com/MathScienceTutor
    Direct Link to The Full Video: www.bit.ly/3zuP2s0

    • @mwilakellys5523
      @mwilakellys5523 2 года назад +3

      awesome

    • @noah5756
      @noah5756 2 года назад +2

      very helpful!

    • @yousufzohair4342
      @yousufzohair4342 10 месяцев назад +2

      I cannot become A member.. It is something to do with my country.. What can I do to watch full videos?

    • @Ismaelkauga
      @Ismaelkauga 9 месяцев назад +1

      I couldn't access the full 1 hour video

    • @martial-kr9yc
      @martial-kr9yc 8 месяцев назад +4

      Hello sir,if you don't mind you can feel free to let us enjoy the full lesson just here . humbly

  • @NASAFanboy
    @NASAFanboy 2 года назад +962

    Trig sub is one of the hardest integration techniques to learn and you explain it in such an easy to follow way.

    • @citizencj3389
      @citizencj3389 2 года назад +159

      It's actually the hardest to learn because you need full knowledge of trig identities, sohcahtoa, and even inverse trig functions to solve some of these.

    • @cheekybum1513
      @cheekybum1513 2 года назад +56

      @@citizencj3389 bro exactly
      It's occured to me that I never learned or probably forgot all those identities

    • @mahmoudeabdel-aziz7456
      @mahmoudeabdel-aziz7456 2 года назад +17

      @@citizencj3389 dude you have written what i needed in your comment , you saved my life , i will fight for you

    • @deshawnburton7114
      @deshawnburton7114 2 года назад +21

      Right.. its almost like the lecturers teach us in a difficult way in purpose and thus guy just tells us wassup without the bullshi*

    • @BraceGD
      @BraceGD Год назад +6

      Just goes on to show that calculus is easy if you have the right teacher

  • @janine9062
    @janine9062 3 года назад +951

    I just want you to know that I’ve got a 96 in Integral and Differential Calculus because of you! I can’t thank you enough!

    • @charlest2858
      @charlest2858 3 года назад +22

      How did you do it?

    • @izzahzamri2267
      @izzahzamri2267 3 года назад +18

      that's really powerful!

    • @abmsirpaathshala3175
      @abmsirpaathshala3175 3 года назад +3

      ruclips.net/video/UqSifKM5eTg/видео.html

    • @VergilPeterson
      @VergilPeterson 3 года назад +23

      Lucky you. I don’t think I can make it past calc 2

    • @jonathancurren5214
      @jonathancurren5214 3 года назад +45

      @@VergilPeterson yeah I am in Calc II at Ohio State, it’s terrible. I have a midterm this Friday and I’ve gotten a 45/100 and 49/100 on both my practice exams😐

  • @restfulcube-notyet
    @restfulcube-notyet 3 года назад +2279

    integration used to be so much simpler ... and then this came along

    • @jonassal2676
      @jonassal2676 2 года назад +24

      What the heck!?

    • @khurshidbekkk2647
      @khurshidbekkk2647 Год назад +17

      I feel you man😢

    • @MichealQuinm
      @MichealQuinm Год назад +256

      Calc II wasn’t the same after the trig sub dlc

    • @mostafasoliman6745
      @mostafasoliman6745 Год назад +5

      ​@@khurshidbekkk2647 where are fromm buddy
      U look like coming from 19th Egypt 😅

    • @khurshidbekkk2647
      @khurshidbekkk2647 Год назад +3

      @@mostafasoliman6745 i am from Uzbekistan

  • @daughteroftheking3220
    @daughteroftheking3220 3 года назад +1311

    Honestly, I hope you succeed in whatever things you do. I wish you many more blessings in your life. You mean so much to your students. I hope you freaking go viral and gain many supporters. I don't understand how celebrities could be going viral for doing the mundane things, but our educators can't even get the recognition they deserve, as they are the ones actually changing lives. You guys deserve an award for all your hard work. I guarantee you that your hard work and dedication don't go unnoticed. We see you grinding and hustling, so thank you from the bottom of my heart. You are literally an underrated genius. Thank you so much, even words can't express how grateful we are for you. You always pull through at the right time for us all. Don't ever stop posting! I don't think I will stop watching your videos even if I finish school, just for the sake of learning and sharpening my skills. Knowledge is power and you inspire so many of us to keep learning no matter what.

    • @eri4232
      @eri4232 3 года назад +42

      you’re right, he has helped many of us who can’t afford tutoring and he has covered a wide aspect of subjects and topics, he deserves an award

    • @moof1232
      @moof1232 2 года назад +6

      well spoken

    • @t-gler4615
      @t-gler4615 2 года назад +2

      Studying is not fun and entertaining but music is entertainment thays why videos go viral

    • @Stickman_Productions
      @Stickman_Productions 2 года назад +5

      @@t-gler4615 studying is fun when you're doing it independently

    • @t-gler4615
      @t-gler4615 2 года назад +1

      @@Stickman_Productions we talking about maths

  • @jasonjackson4555
    @jasonjackson4555 3 года назад +366

    I wish this channel had been around when I was in undergrad. I remember watching my professor explain this and wondering why this class was a requirement for Econ at UCLA. Now, many years later, I’m still waiting for a chance to show off my trig substitution skills. I’m getting my MBA in 2 weeks and I didn’t need it there either.

    • @BaoBao-im4zv
      @BaoBao-im4zv 2 года назад +11

      I am studying econ and i was asking myself why should i see this kind of math but here i am seeing, this won't help with anything in the future too.

    • @karstenkunneman5219
      @karstenkunneman5219 2 года назад +15

      Did you use it in those last 2 weeks?

    • @paulveba6225
      @paulveba6225 Год назад +6

      @@karstenkunneman5219 Im dead

    • @Psowi
      @Psowi Год назад +1

      Maybe because you arent studying TEM

    • @mphIII
      @mphIII Год назад +4

      @@Psowi exactly, you just proved why non STEM students shouldn't have to take calculus

  • @phoen1x900
    @phoen1x900 3 месяца назад +45

    bro literally named himself organic chemistry teacher then started teaching whatever tf we need
    Trust me he is the best guy to learn

  • @aidenx3vv
    @aidenx3vv Год назад +134

    When it comes to finding the missing side of the right triangle, it's worth noting that it always turns out to be the square root from the original integral that made us need to do a trig sub in the first place

    • @georgesadler7830
      @georgesadler7830 Год назад +7

      Please watch Professor V, Integral of the Day Playlist for more on Techniques of Integration in Calculus. Pattern recognition is also needed for Trig Substitution.

  • @Coreyahno
    @Coreyahno 3 года назад +182

    For all you people struggling through Calc 2 right now, just keep at it and take comfort in the fact that Calc 3 and Differential Equations won’t be nearly as bad. I’m in D.E right now and it’s actually kind of fun!

    • @Sam2rreal
      @Sam2rreal 3 года назад +8

      fr?

    • @johnlouiederayunan7851
      @johnlouiederayunan7851 2 года назад +25

      thanks. barely at the edge rn

    • @cheekybum1513
      @cheekybum1513 2 года назад +18

      that's exactly what I heard at my school. People say Calc 2 is the hardest calc class

    • @tek1645
      @tek1645 2 года назад +10

      Unfortunately I only need calc 1 and 2

    • @GIGATHEBOT
      @GIGATHEBOT 9 месяцев назад

      oh boy, but than i got continuous time systems after that.

  • @pixelninja5766
    @pixelninja5766 3 года назад +386

    2:38 "now we gotta do some math" legendary

    • @codywhite9979
      @codywhite9979 2 года назад +12

      Me: "...that's why I'm here."

    • @Joseph973
      @Joseph973 8 месяцев назад +9

      18:24 "What was I thinking?" ...Me after every math test

    • @mosantw2014
      @mosantw2014 6 месяцев назад

      "The hard part's over"
      Me: nope, the hard part beings😢

    • @AzureSwiper
      @AzureSwiper Месяц назад

      "Now we gotta do some maff" 🤣

  • @Diamond-vy1lx
    @Diamond-vy1lx 3 года назад +674

    This is what online math classes should be like

  • @AV4Life
    @AV4Life 5 месяцев назад +23

    Organic chemistry tutor, Professor Leonard, & NancyPi. The terrific trio for carrying STEM students.

  • @nathankraft6102
    @nathankraft6102 3 года назад +17

    I watched an hour long lecture from my professor and did not understand this but watched 2 minutes of your video and I already understand it better. Thank you for your service to confused college students.

    • @Mattletic
      @Mattletic 2 года назад +1

      That's exactly what I was saying. I just spent 75 minutes in class, and understand the subject more in the first two minutes of this video, then my teacher has taught me in the whole chapter

  • @nuridaw9586
    @nuridaw9586 Год назад +20

    The last time I learned Calculus was almost 20 years ago, and this year I need to tutor Calculus. Your videos really really helped me. You are really gifted with being able to explain complex things in simple ways. THANK YOU.

    • @josuequintero-td5gh
      @josuequintero-td5gh Год назад

      This might be a stupid question but do you remember anything from 20 years ago?

    • @nuridaw9586
      @nuridaw9586 Год назад +1

      @@josuequintero-td5gh Yes, generally I do. But if you are asking whether I remember what I learned about Calculus 20 years ago, yes I remember the basics.

  • @calebnguyen7348
    @calebnguyen7348 3 года назад +53

    I watched this video an hour before my test in desperate need of help since I did not understand it. I saw a question and I got it right because of you. Thank you so much!

  • @ihasknees8730
    @ihasknees8730 Месяц назад

    The absolute greatest person to ever exist. This one has single handedly raised every calculus and chemistry pass rate across the globe. We all love you.

  • @donpowers8726
    @donpowers8726 Месяц назад +1

    This is great video. The presenter goes along very well and does not edit out the few small oopps that we all do when solving equations. Well done . Thanks

  • @PunmasterSTP
    @PunmasterSTP Год назад +9

    I tutor calculus students and yesterday I realized I was rusty on trig substitution. This video was just what I needed; thanks for sharing!

  • @maryconnot3424
    @maryconnot3424 3 года назад +35

    I would just like to say thank you to the organic chemistry tutor! You are the greatest! His videos have helped me with bio, chem, calc 1 and 2, and physics

  • @kaevindixon77
    @kaevindixon77 3 года назад +34

    Love this guy but at 3:30 he dropped the square of sin in the denominator of the integral. Just for people that are trying to follow along

    • @MD-cy7lb
      @MD-cy7lb 2 года назад +6

      He corrected that in 4.12 mintes

    • @yuunaa7827
      @yuunaa7827 2 года назад

      @@MD-cy7lb but why does the numerator still 4(1-sin^2theta), shouldn't it be 4(1-sin theta) only because 2^2 is already 4?

  • @avunz125
    @avunz125 3 года назад +26

    This dude is covering calc2 while I'm doing it. It's one of the best feeling in the world.

  • @Allahu_Akbar_the_one
    @Allahu_Akbar_the_one Год назад +27

    damn-can't get away without knowing my Trig anymore. Looks like I have to do a whole relearning!

    • @generalmalaise2930
      @generalmalaise2930 Год назад +4

      yep exactly. ive been alright with my surface-ish recall of trig until this lesson lmao

    • @Amaru1111
      @Amaru1111 7 месяцев назад

      ​@@generalmalaise2930haha wait until you need to know reduction formulas and power reducing rules

  • @Mariamak98
    @Mariamak98 3 года назад +13

    🏃🏻‍♀️5 hours till my exam, i am grateful that u uploaded this today , thankkkk uuu

  • @eri4232
    @eri4232 3 года назад +9

    I’m so thankful you made a video on this, I went crazy trying to understand this when the textbook just put it with no explanations

  • @batzuljohnthomas6094
    @batzuljohnthomas6094 2 года назад +4

    No way, every question I have I look for it and your channel appears, I will definitely dedicate my title to you when I graduate, thanks for everything!

  • @elliewolcott6254
    @elliewolcott6254 2 года назад +13

    Revisiting this for calc 3. Thanks so much for your videos! They help A TON.

  • @SavannahStotts
    @SavannahStotts 9 месяцев назад

    this channel has single handedly saved my grade in math so many times

  • @bata3258
    @bata3258 7 месяцев назад +2

    Best revision channel ngl

  • @lyndseystrait1513
    @lyndseystrait1513 8 месяцев назад +4

    1:12 Full list of trig formats & associated x=a formulas. Problem 1 (1:18-8:45); Problem 2 (9:02-19:24)

  • @philipsoyoo6862
    @philipsoyoo6862 Год назад +7

    I am going to achieve...above average because of you

  • @jpmcfrosty
    @jpmcfrosty 2 года назад +1

    This chapter right here, is the core difficulty of all embodiment of Calculus holy shit

  • @puremaths2444
    @puremaths2444 3 года назад +56

    A part of my school fees should be given to this guy,,

  • @emmafoster7330
    @emmafoster7330 Год назад +3

    This helped me so much with my Cal2 homework! Keep it up man!

  • @preston7246
    @preston7246 Год назад +1

    it is 8 pm I have a calc 2 final tomorrow morning and I'm just now trying to finally learn trig subs.

    • @matthewhrndz
      @matthewhrndz Год назад

      how'd you do?

    • @preston7246
      @preston7246 Год назад +1

      @@matthewhrndz I got a 151/200 on the final and passed the class with a 76

    • @matthewhrndz
      @matthewhrndz Год назад

      @@preston7246 aye let's gooo, i have my calc 2 final next wednesday

    • @preston7246
      @preston7246 Год назад +1

      @@matthewhrndz nice nice good luck on it man

  • @theengineer9910
    @theengineer9910 Год назад +1

    In TheOrganicChemistryTutor We Trust

  • @chump_
    @chump_ Год назад +1

    i just like listening to your voice honestly

  • @ateezstanhell
    @ateezstanhell Год назад

    lmao you are my savior istg i have a test on thursday and im PANICKING bc i completely zoned out these past few weeks i needed a solid lesson on how to do these thank you

  • @xXRedTheDragonXx
    @xXRedTheDragonXx 2 года назад +2

    Thank you for this video! I can't understand what my calculus professor is talking about sometimes and your videos really help!!

  • @rnz9999
    @rnz9999 3 года назад +4

    This came out at the right time, I have an exam about this tomorrow, thanks

  • @AverageSkoomaEnjoyer1
    @AverageSkoomaEnjoyer1 Год назад

    This just makes me realize how bad my prof actually is. We have been blessed with your existence. Tysm!

  • @ΔημήτρηςΜίαρης-Κοιλάδης

    Helpful content as such shouldn't be locked behind a paywall.

  • @divineattai8291
    @divineattai8291 День назад

    This guy u turn mathematics to water ...why are u this good and also in teaching

  • @helenemso32
    @helenemso32 10 месяцев назад +1

    very clear lecture thank you u are amazing keep working the organic chemistry

  • @jbjc3924
    @jbjc3924 Месяц назад

    at 4:35 when you have cos^2 / sin^2, seems more intuitive to see that as cot^2 rather than 1-sin^2 / sin^2

  • @unregistereduser5929
    @unregistereduser5929 2 года назад +4

    Thank you so much! Your channel always pulls me through trouble, I'm grateful for your hard work!!

  • @danielzuniga6570
    @danielzuniga6570 2 года назад

    You are the reason I am understanding calc, bless you

  • @shmrzwdd
    @shmrzwdd 3 года назад +13

    Thankyou so much ! 💜 Its exactly what i need

  • @rorymackinnon6133
    @rorymackinnon6133 2 года назад

    You are the best teacher I ever had. Thank you for everything you do. Making it look so easy is probably the hardest part, but it makes all the difference. Screw kahn academy.

  • @CrazyMarkStudios
    @CrazyMarkStudios Год назад +2

    7:23 Timestamp

  • @hisuii
    @hisuii Год назад

    god bless bro i got a calculus exam in 8 hours this just saved my ass

  • @user-fk5di4me9c
    @user-fk5di4me9c 2 года назад +2

    This is by all means the hardest shit I have ever studied it!

  • @afaqahmad8674
    @afaqahmad8674 3 года назад +1

    Thank u so much! You have proved that maths can be learned virtually as effective as physically.

  • @alexcoello4288
    @alexcoello4288 11 месяцев назад

    You're a literal saint dude
    Thank you for all of your videos you have helped me tremendously with stats and calc!

  • @utilizator1701
    @utilizator1701 3 года назад +4

    8:03 whoa! Much simpler method to determin tan(arcsin(x/2)), cos(arcsin(x/2)) etc. Until now I have used trigonometric relations and calculus to determin those functions.

  • @Loogia
    @Loogia Год назад +1

    Never took a trig class before, so y'all already know I'm having a great time in calculus 😂

  • @Rahmanyboss
    @Rahmanyboss Год назад +1

    2:37 was my favorite part 👌

  • @J_3564
    @J_3564 Год назад

    This channel is the goat

  • @mohammadshabih5293
    @mohammadshabih5293 3 года назад +4

    Bruh I was confused about this and now you uploadef this🥺

  • @MotloungPule-y9u
    @MotloungPule-y9u 5 месяцев назад

    organic Chemistry tutor you deserve something huge from the world wide🤑🥰

  • @McGregorofManchester
    @McGregorofManchester Год назад

    You are an amazing interllect and you deserve an Academic Golden Nobel price for your amazing work...keep going man be blessed, be healthy..thanks.

  • @niyomizeropierrecelestin6018
    @niyomizeropierrecelestin6018 2 года назад

    Thank you very much.
    I already understand what was complicated to me.
    May God bless you 🙏.

  • @clementramasela4428
    @clementramasela4428 Месяц назад +61

    i might be cooked ngl

    • @monk5058
      @monk5058 Месяц назад +3

      Same

    • @bungle5899
      @bungle5899 10 дней назад +10

      I’m 100% cooked . Marinated, baked, sauteed and fried . Seasoned even

    • @blessingmagombedze7678
      @blessingmagombedze7678 10 дней назад

      @@bungle5899me… my test tomorrow

    • @Symmz
      @Symmz 5 дней назад +1

      Exam today. Im heavily cooked

    • @bungle5899
      @bungle5899 4 дня назад +1

      @symmz wait I also had this exam today , i think I at least got a 50 😎

  • @renaaa_8913
    @renaaa_8913 Год назад

    Better than my professor!

  • @aralia.
    @aralia. 3 года назад +1

    my test is in an hour thank you so so much!!!

  • @giuseppemalaguti435
    @giuseppemalaguti435 2 года назад +1

    posto x=2sint...ho -ctgarcsin(x/2)-arcsin(x/2)....-sqrt(4-x^2)/x-arcsin(x/2)

  • @lettuce1325
    @lettuce1325 2 года назад

    I have not met a professor who you have not routinely outclassed

  • @SHAHRIARMOSTAFA-il5fy
    @SHAHRIARMOSTAFA-il5fy 8 месяцев назад

    please do a video on gamma and beta functions too i love your channel

  • @soapygaming1562
    @soapygaming1562 3 года назад

    You are a lord and savior I was stuck on this

  • @JabulaniSimapempa
    @JabulaniSimapempa Месяц назад

    Happy teacher's day JG🎉🎉🎉

  • @amanielmeharena3885
    @amanielmeharena3885 Год назад +1

    Tried the Third problem at the end, solved it, ty!

  • @georgesadler7830
    @georgesadler7830 2 года назад +3

    Professor Organic Chemistry Tutor, thank you for another excellent video/lecture on Trigonometric Substitution in Calculus Two. All students/nonstudents should have a solid understanding of Trigonometry before studying Trig Substitution.. This is an error free video/lecture on RUclips TV with the Organic Chemistry Tutor.

  • @lonkbadonk3195
    @lonkbadonk3195 2 года назад

    the god tier tutor of the internet

  • @robiriggin1112
    @robiriggin1112 3 года назад +3

    I made a 94 on shell and washer method because of this man. I hope I can do the same with trig sub and integration by parts

  • @JassCodes
    @JassCodes 3 года назад +4

    You are our life saviour !

  • @assaineindustries
    @assaineindustries 3 года назад +2

    Thanks professor JG

  • @abhinavcheedella4296
    @abhinavcheedella4296 3 года назад +16

    I lowkey have been watching these even when im not even in math anymore so that i can keep my math skills

  • @NaftaliSpodek
    @NaftaliSpodek Год назад

    It's important to make sure in every step That the domains are reasonable In the substitution
    For example The square root of sec²( theta) Has to be positive So we need to make sure in the substitution To make the restrictions positive

  • @abcdefghij7256
    @abcdefghij7256 2 года назад

    Thank you for this lesson organic chem!

  • @holyshit922
    @holyshit922 Год назад

    I with integration by parts am able to calculate it in my mind a lot faster than 20 minutes

  • @MaharaMsefula
    @MaharaMsefula 7 месяцев назад

    The complexity in this technique 😮

  • @I61void
    @I61void Год назад

    I think I understood everything up to turning theta into arcsin(x/2)

  • @mattjw16
    @mattjw16 8 месяцев назад +2

    For the last one, why can’t you do 9sec^3(arctan(x/3)) - 27sec(arctan(x/3)) + C?

  • @topgminset420
    @topgminset420 2 года назад

    love ur videos man thanks very much my whole confusion is gone

  • @ayahraisha5234
    @ayahraisha5234 3 года назад +3

    you are so great its unfortunate that i can't find the "join" option on your channel :( i really wanna have access to your full vids

  • @karycolin9046
    @karycolin9046 2 года назад

    Thanks for this amazing video! Regards from Mexico!

  • @DesertSoldier_ii
    @DesertSoldier_ii 2 года назад

    You’re a life saver

  • @adamreisenauer3141
    @adamreisenauer3141 18 дней назад

    Legit was going to crash out before I learned this!

  • @desiledolapo9012
    @desiledolapo9012 3 года назад +5

    Can you do a video for crystal systems pleaseee😭😭😭 Thanks for every one of your video btw, they help a lot!

  • @izzyheslop7522
    @izzyheslop7522 2 года назад

    this video saved me

  • @theforexacademy1827
    @theforexacademy1827 Год назад

    Where is the square of the sine in the denominator? U omitted it !

  • @deloybandawe421
    @deloybandawe421 5 месяцев назад +1

    Thanks😊

  • @wakuwaku3190
    @wakuwaku3190 10 месяцев назад

    MERRY CHRISTMAS SIR!

  • @anestismoutafidis4575
    @anestismoutafidis4575 Год назад

    => Int [2/x -1] • dx

  • @laibakhan8380
    @laibakhan8380 2 года назад

    I don't know how to thank you! 😭😭😭😭❤️❤️

  • @JohnSmith-hp9ds
    @JohnSmith-hp9ds 2 года назад

    Thank you so much
    You're the absolute best

  • @aiman_shakir
    @aiman_shakir Год назад

    Thank you so much for the explanation!! 🥰🥰

  • @cloudyyish
    @cloudyyish 2 года назад

    thanks so much for ur help homie

  • @jinnjinn5567
    @jinnjinn5567 2 года назад +2

    Students can also use the derivatives of inverse trig functions to recall the proper trig substitutions
    d/dx arcsin(x) = 1/sqrt(1-x^2)
    d/dx arctan(x) = 1/(1+x^2)
    d/dx arcsec(x) = 1/(x * sqrt(x^2 - 1))
    hyperbolic substitutions, too
    a*sinh(u) for a*tan(u)
    a*tanh(u) for a*sin(u)
    a*cosh(u) for a*sec(u)
    And you’ll see similar patterns with derivatives of hyperbolic trig functions

  • @Kat-37i9
    @Kat-37i9 2 года назад

    When a 20 minute video teaches you more then a week of class

  • @doeverything7997
    @doeverything7997 8 месяцев назад +2

    17:28 - You lost your -27 sec theta