Trigonometric Integrals

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  • @TheOrganicChemistryTutor
    @TheOrganicChemistryTutor  2 года назад +93

    Full 1 Hour Video on Patreon: www.patreon.com/MathScienceTutor
    Direct Link to The Full Video: bit.ly/3zxSr9g

  • @pfact0593
    @pfact0593 3 года назад +1205

    When i graduate.. i wanna thank 'organic chemistry' RUclips channel it help me a lot thanks man

    • @primevandal2769
      @primevandal2769 3 года назад +15

      Can u tank him for me

    • @mariasemaan8921
      @mariasemaan8921 3 года назад +4

      me too

    • @landrypreston284
      @landrypreston284 3 года назад

      Sorry to be so offtopic but does anybody know of a tool to log back into an Instagram account?
      I somehow lost the login password. I love any assistance you can give me

    • @PierceMartinez
      @PierceMartinez 2 года назад +13

      I owe everything to RUclips calc vids, especially those done by this incredible individual.

    • @yanodat2926
      @yanodat2926 2 года назад +1

      This man is a god at helping me know calc 2

  • @fatdogonsand
    @fatdogonsand 2 года назад +545

    I just sat back to myself and said "i did it, that's cool." I never would have been able to do it without these videos. you are the best, and i appreciate you beyond words. i hope everyday is a great day for you.

    • @lelomambueliane4915
      @lelomambueliane4915 2 года назад

      Click here to view ruclips.net/video/Mar53onVvMo/видео.html

  • @SebastianDauod
    @SebastianDauod 2 года назад +243

    Its 150am and my exam is at 1030am... pray for me everyone. I use this guy all the time and he always helps. I'll be back to update after the exam
    UPDATEEE: Hey guys I did not thunk this would get so much traction. I passed the test and did well! Calculus 2 as a whole is hard and I absolutely crushed math throughout my life. However work hard , study with friends, USE A WHITEBOARD, get some sleep too. 👍🙏

  • @troyguererro0898
    @troyguererro0898 Год назад +37

    I cannot find your video where I want to thank you for your videos when I was in 1st year college. I just saw my name on the board passers of mechanical engineers yesterday. Thank you organic chemistry ❤️.
    To anyone watching this vid. May your dreams come true. DON'T STOP BELIEVING

  • @noornahar1933
    @noornahar1933 4 месяца назад +16

    Nah man if u are not getting over a million dollars out of each of your videos youtube has underrated u. U deserve so damn much for how much you have and are doing fo us and saving millions of exams over here. Salute to u sir!

  • @bmr2104
    @bmr2104 3 года назад +310

    You explain everything really well and your voice is sooo good. Thank you. Never stop doing what you're doing now.

  • @danielsosa665
    @danielsosa665 Год назад +72

    You are really talented man! It's so easy to follow your line of thought. Precise and clear speech at a perfect pace. I can't thank you enough. Hands down best math teacher.

  • @farhanishraq5812
    @farhanishraq5812 2 года назад +266

    Tomorrow is my exam and i got really confused about these integrations and this channel helped me a lot.
    Thank you so so so much

  • @Gnisselb_O
    @Gnisselb_O 3 года назад +82

    Thank you very much sir. I was so frustrated in the class, I felt like giving up ; A Nigerian learning calculus in Chinese language 😂😂😂. But you uploaded this video when I needed it the most. I can now happily study calculus.

    • @chavasinyadalmasgulema885
      @chavasinyadalmasgulema885 3 года назад +1

      Hello

    • @spicyshizz2850
      @spicyshizz2850 2 года назад +3

      LMaoo wow that seems difficult, do you know any Chinese?

    • @Gnisselb_O
      @Gnisselb_O 2 года назад +4

      @@spicyshizz2850 I stay in China, why shouldn’t I 😅?

    • @drsuenscooetze4507
      @drsuenscooetze4507 2 года назад +1

      Could you be Mrs me 😂👑

    • @Gnisselb_O
      @Gnisselb_O 2 года назад +1

      @@drsuenscooetze4507 hahahaha. It’s actually miss me. ( to miss somebody)😜😜😜

  • @PunmasterSTP
    @PunmasterSTP Год назад +36

    I needed to review how to handle various powers of trig functions in integrals in order to tutor some calculus students, and this video was exactly what I needed. Thank you so much for making and sharing such high-quality material!

  • @Robert-el2mf
    @Robert-el2mf 3 года назад +60

    Your timing is impeccable

    • @fernvill
      @fernvill 3 года назад +1

      And totally calculated

  • @shedrachchimezie5158
    @shedrachchimezie5158 Год назад +13

    This man has been my life saver in this semester maths, I just finished writing my exam now and am expecting a good grade, all credit to this man

  • @Anonymous-jj1re
    @Anonymous-jj1re 3 года назад +43

    Thank you for extending the video beyond the original non membership one you put out before

    • @lelomambueliane4915
      @lelomambueliane4915 2 года назад

      Click here to view ruclips.net/video/Mar53onVvMo/видео.html

  • @preston2078
    @preston2078 2 года назад +68

    i watched your video on getting straight As. the most interesting tip you made in my opinion was to read the textbook ahead of time. I love that idea, but don't want to use a textbook so I follow along with you before learning about it in lecture. You've thought me just as much, or more than all my recent stem class teachers/profs recently.

    • @lelomambueliane4915
      @lelomambueliane4915 2 года назад

      Click here to view ruclips.net/video/Mar53onVvMo/видео.html

  • @Rahmanyboss
    @Rahmanyboss Год назад +56

    You are the reason I’m passing calc 2! Keep up the great work!!!

    • @Rushman666
      @Rushman666 Год назад +3

      Is this calc 2 material?

    • @marckx1254
      @marckx1254 Год назад

      for me yeah@@Rushman666

    • @tavistafford8010
      @tavistafford8010 11 месяцев назад +6

      @@Rushman666 Yeah it is. I am in Calc 2, and we are doing this on our third week of class.

    • @romeo9015
      @romeo9015 11 месяцев назад +1

      @@Rushman666 i attend GSU and this is in fact Calc 2 material. Third week of class.

    • @kendricnissen6216
      @kendricnissen6216 10 месяцев назад +1

      @@Rushman666yes, this is calculus 2.

  • @visakha5982
    @visakha5982 3 месяца назад +7

    "now go ahead and try that" knowing that no one will succeed😭

  • @hectorcorona9257
    @hectorcorona9257 2 года назад +20

    the day I graduate I will deadass mention the organic chemistry tutor for helping me throughout high school

    • @RetroMaster64
      @RetroMaster64 6 месяцев назад +3

      Bro high school? Dang, I'm doing this my second year of university

  • @DuckGod00
    @DuckGod00 Год назад +10

    It’s 12pm and the test is at 1pm, wish me luck 😭

  • @FLgrown14
    @FLgrown14 3 года назад +45

    Thanks man! I’m reviewing for my final and this is super helpful!

  • @matthewregan5095
    @matthewregan5095 Год назад +3

    I have my calc 2 final in less than 12 hours… last minute studying at its finest 😍
    Everyone wish me luck please cause I’m gonna need it

    • @mahi33333
      @mahi33333 5 месяцев назад

      did u make it omg

  • @SmellyUnfortunate007
    @SmellyUnfortunate007 3 года назад +11

    I just had a test yesterday, and I actually feel confident that I did the problem right.

  • @georgesadler7830
    @georgesadler7830 2 года назад +6

    Professor Organic Chemistry Tutor, thank you for another fantastic video/lecture on Trigonometric Integrals in Calculus Two. These integrals are built off of Trig Identities and pattern recognition. All students in Science and Engineering should memorize all the Trigonometric Identities from Trigonometry. This is an error free video/lecture on RUclips TV with the Organic Chemistry Tutor.

    • @splishysploosh5097
      @splishysploosh5097 День назад

      Georgesadler7830, thank you for yet another amazing comment/remark on this video/lecture on Trigonometric Integrals in Calculus Two. Your statements are well thought out and accurately composed. Anyone who watches Calculus Two videos by Professor Organic Chemistry Tutor should like your comment. This is an error-free comment on RUclips TV on the video/lecture on Trigonometric Integrals in Calculus Two by Professor Organic Chemistry Tutor.

  • @lexihunsucker7067
    @lexihunsucker7067 3 года назад +10

    ngl these make more sense than my professor's notes, thanks my dude you're saving my grade :D

    • @diags_1109
      @diags_1109 2 года назад +1

      well maybe you got it to a :C now

  • @User84367
    @User84367 2 месяца назад +8

    lets all ace calc 2 together

    • @User84367
      @User84367 2 месяца назад

      set your heart ablaze

    • @BaconGator
      @BaconGator Месяц назад

      We ain't doing so well so far.

    • @User84367
      @User84367 Месяц назад

      @@BaconGator definitely harder than expected but fuckit still

    • @BaconGator
      @BaconGator Месяц назад

      @@User84367 fuck it we ball.

    • @User84367
      @User84367 Месяц назад

      @@BaconGator let’s get it

  • @jimmeneses988
    @jimmeneses988 Месяц назад

    Currently taking the integral calculus summerclass in mechanical engineering and the trigo seems so hard to absorb in just small span of days but you're videos always making things so much clear and straight to the point. I will be forever thankful to this channel as it helped me to understand mathematics and science in my highschool years up until my college life now.

  • @Jujo1
    @Jujo1 3 года назад +9

    Hey man please make a separate playlist so that it's easier to find the right lecture at the right time, make a different channel playlist for all integrals..... Great work man big fan!!❣️

    • @farechildd
      @farechildd 3 года назад +3

      He's got a calculus playlist that's in order of how it is typically taught. You should be able to follow along pretty well with that

    • @farechildd
      @farechildd 3 года назад +3

      It's called "New Calculus Video Playlist" and integrals start at video 127.

    • @lelomambueliane4915
      @lelomambueliane4915 2 года назад

      Click here to view ruclips.net/video/Mar53onVvMo/видео.html

  • @stayrigo
    @stayrigo 9 месяцев назад +2

    This is my last highschool exam. Thank you for all your help throughout the years can't wait to come back for UNI content❤

  • @lyndseystrait1513
    @lyndseystrait1513 6 месяцев назад +1

    List of 0:36 trig identities, 1:12 double angle identity, & 1:47 power reducing formulas to memorize

  • @bhaskarroy-jee8482
    @bhaskarroy-jee8482 2 года назад +8

    Thanks it will definitely help me in my JEE preparation as well as my class 12th board exam. Love from india (:

  • @cassiopiarobel9994
    @cassiopiarobel9994 2 года назад +4

    Am grade 12 student.and with out this man I couldn't survive high school.cause all my teachers doesn't even know what they are teaching.i some times wonder if they know what they are talking about .but thanks for you i can understand the basics.may God bless you.👏👏👏👏👏

  • @brandoncarrillo7486
    @brandoncarrillo7486 5 месяцев назад +2

    I did not understand this during my class so Thank You a lot!!!. I feel like a pro now 😎

  • @danieltracton3888
    @danieltracton3888 2 года назад +1

    you are literally the patron saint of all science students.

  • @user-ve7no9tj7c
    @user-ve7no9tj7c 2 года назад +7

    in the exercise at 14:00 (sin^5x*cos^3x*dx), if you use u=cosx and du=-sinx*dx, is the answer → - cos^4x/4 + cos^6x/3 - cos^8x/8 + C ?

    • @user-cp1lo8sn9u
      @user-cp1lo8sn9u 5 месяцев назад

      i did it the same way and i got that as the answer 😭

  • @princekwejoyeboah7695
    @princekwejoyeboah7695 10 дней назад

    Thanks very much for helping understand this concept.
    I always come here for easy understanding after am been confused in lectures
    May your creator bless you

  • @Rose-rp6sx
    @Rose-rp6sx 5 месяцев назад +1

    mechanical engineering major here. thank you for this video, it really helped me out a lot!

  • @user-cd9be4qj4w
    @user-cd9be4qj4w 4 месяца назад +1

    Thank you for making Mr graduate with an A in advanced calculus

  • @abrahamflores1111
    @abrahamflores1111 3 месяца назад +7

    I want to adopt bro as my father

  • @barerparsley3311
    @barerparsley3311 Год назад +2

    i just realized i literally proved the power reducing formulas in class today while trying to find the integral of sin^2 and cos^2 thats sick

  • @kengabarakawyclif2394
    @kengabarakawyclif2394 2 года назад +2

    You are amazing....from AFRICA...KENYA

  • @jondis8588
    @jondis8588 2 года назад +5

    I can't understand which should i let u :((

  • @farhatfatima1168
    @farhatfatima1168 2 года назад +8

    Thank you so so much for making these videos which help me alot n even more than my professor....may God bless you sir

    • @lelomambueliane4915
      @lelomambueliane4915 2 года назад

      Click here to view ruclips.net/video/Mar53onVvMo/видео.html

  • @kennethcox6895
    @kennethcox6895 3 года назад +6

    Thanks for what you are doing dude.

  • @theuberman7170
    @theuberman7170 2 года назад +1

    You were forged by the Gods of knowledge & wisdom!

  • @danieldegefe2727
    @danieldegefe2727 Год назад

    How to thank the people who do like you.
    There is no one in this world who is talented just like you it is amazing.

  • @bernadettelola638
    @bernadettelola638 3 года назад +8

    That's what I was looking for. Thank you.

  • @christopherteo4446
    @christopherteo4446 2 года назад

    your my hero without your videos I can't survive my calculus 1 and 2

  • @ThePiMan0903
    @ThePiMan0903 Год назад +3

    Thanks for this video The Organic Chemistry Tutor! It was really helpful!

  • @selmarahal1458
    @selmarahal1458 2 года назад +2

    Dude saving my life more than a snickers on hypoglycemia , one day ill pay you back

  • @katiemacisaac5817
    @katiemacisaac5817 2 года назад +1

    You are every stem majors hero

  • @sonerex8079
    @sonerex8079 3 года назад +1

    So i have this mid exam next week and suddenly you've uploaded this video thaaaaaaaaaaaanks bro you just saved me

  • @blenzewdu647
    @blenzewdu647 11 месяцев назад

    Ultimate life saver before exams!

  • @Mayandajohn2005
    @Mayandajohn2005 2 года назад +2

    Cheers man you made me to become the God of math

  • @mrsweeteatft
    @mrsweeteatft Год назад +3

    this video gave me a 20 IQ boost

  • @anoopgill7245
    @anoopgill7245 Год назад +16

    at 14:00 why can't we split up sin instead? Does it work to do (1-cos^2)^2 for sin^4 and then have cos^3 and the other sign left? Then we could use u as cos and cancel the other sin out?

    • @vigoolz241
      @vigoolz241 Год назад +7

      you can do it but it's more work

    • @kara5202
      @kara5202 Год назад

      @@vigoolz241 I did it but the answer is not the same. If you input the answer to a drawing system they follow the same path but with the cosine its -1/24 lower than the with the sin version at all times. So the answer is incorrect...

  • @bestyoueverhad.2408
    @bestyoueverhad.2408 3 года назад

    You and TrevTutor are the best here on YT.

  • @cbbuntz
    @cbbuntz 2 года назад +2

    Memorize your chebyshev polynomials, folks. In matlab, I have functions that generate chebyshev matrices and the inverses to convert between cos nx and cos^n x. I've found that asking it to integrate cos^n(x) takes way more processing power than just converting it to the equivalent chebyshev form and then integrating.
    Also useful for definite integrals of the form sin^a(x)*cos^b(x) or sin^a(x)*cos(bx) (or similar) is the beta function
    en.wikipedia.org/wiki/Beta_function#Reciprocal_beta_function
    Both are closely related and you can modify one to get the other.

  • @joseignacioblancogarcia-va8276
    @joseignacioblancogarcia-va8276 2 года назад +1

    Sir, you are the hero we all needed.

  • @mmd-wt5eq
    @mmd-wt5eq Год назад

    In 25:00 you can just easly add 4 and divide by 4, so you have inside integral:
    4sin^2cos^2
    And that is
    (2sin cos)^2
    Which is
    (sin2x)^2

  • @kagishokhumisi4565
    @kagishokhumisi4565 3 года назад +2

    Now everything is clear
    Thank you very much Sir

  • @scoopduna
    @scoopduna 3 года назад +10

    I would recommend going the extra step in some of your less popular videos and include more difficult problems towards the end. I would have been very happy to see a sec^2 x integration in this video. Keep it up though, overall you do a fantastic job with your videos.

    • @lelomambueliane4915
      @lelomambueliane4915 2 года назад

      Click here to view ruclips.net/video/Mar53onVvMo/видео.html

  • @desiledolapo9012
    @desiledolapo9012 3 года назад +8

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

    • @lelomambueliane4915
      @lelomambueliane4915 2 года назад

      Click here to view ruclips.net/video/Mar53onVvMo/видео.html

  • @princechegwe
    @princechegwe Месяц назад

    Thanks a bunch man. You have simplified calculus for me 😁.

  • @DarrenDIY
    @DarrenDIY 3 года назад +1

    Give this man a nobel prize

  • @rajkumarisankhe3601
    @rajkumarisankhe3601 9 месяцев назад

    For cos raised to some power m multiplied with sin raised to some n, you can also simply use Wallis formula, it will save a lot of time, you will come across this formula in first year maths, or in 11/12th grade if you’re a jee student.

  • @mridulboro7467
    @mridulboro7467 2 года назад +1

    This is awesome. Thanks alot sir. I was struggling with those trig function. Now its clear...

  • @CharlesMosesEmeruka-kz9xt
    @CharlesMosesEmeruka-kz9xt 8 месяцев назад

    This RUclips channel is just fantastic! It's so so helpful to me. I love it.

  • @solascriptura911
    @solascriptura911 3 года назад

    This man is without doubt, a terrible genius

  • @dapha1623
    @dapha1623 Год назад

    omg....few days ago I legit spent almost half an hour solving the advanced type of questions. I HATED solving those equations. Now I enjoy it sm 😀😀😀 surprise surprise, learning from the basic do wonders.

  • @chrisbernard388
    @chrisbernard388 2 года назад +1

    Like the way you explain this Mathematical concepts. I like you and be blessed. You always my teacher in this area of calculus.

  • @stogam3550
    @stogam3550 7 месяцев назад +3

    Thanks I'm electrical engineering from Iraq ❤❤❤

    • @koskobirok9760
      @koskobirok9760 6 месяцев назад +1

      Which university?

    • @stogam3550
      @stogam3550 6 месяцев назад +1

      @@koskobirok9760 why

    • @koskobirok9760
      @koskobirok9760 6 месяцев назад

      @@stogam3550 cuzz im in the same college in iraqi kurdstan... So i thought maybe u are in the same uni that im in..

    • @stogam3550
      @stogam3550 6 месяцев назад +1

      @@koskobirok9760 Now I understand, no, I am at Tikrit University

    • @koskobirok9760
      @koskobirok9760 6 месяцев назад

      @@stogam3550 im in sulaimani university

  • @ahmedmamdouh8523
    @ahmedmamdouh8523 2 года назад +2

    When i graduate i wanna send a copy of my degree certificate to you ❤️

  • @collinceomondi4148
    @collinceomondi4148 3 года назад +3

    Your videos are really helping,,I like them👍

  • @shano494
    @shano494 8 месяцев назад +1

    guys when do we know we use the U rule? and a question why did we sometimes in the du=dx part took the thing with dx under du and sometimes we didnt ?

  • @user-bi5gh8no6q
    @user-bi5gh8no6q Год назад

    you're my go to for all things maths - thank you so much!! saving me yet again

  • @mandarinD
    @mandarinD 3 года назад +7

    Thank you!

  • @godhera5116
    @godhera5116 2 года назад

    Thank you from Mauritius 🇲🇺

  • @masmirahintannoviana8940
    @masmirahintannoviana8940 2 года назад +2

    Thank you sir... it's really help me to solve the trigonometry integration

    • @lelomambueliane4915
      @lelomambueliane4915 2 года назад

      Click here to view ruclips.net/video/Mar53onVvMo/видео.html

  • @BsakerXStar
    @BsakerXStar 3 дня назад

    Thanks man,you always pull through

  • @jonah.4240
    @jonah.4240 2 года назад +2

    i've never heard them speak in normal speed before, i always have the vids on 1.5x bcz my exam would be in the next 24 hrs 💀💀💀💀

  • @hiraethvoice348
    @hiraethvoice348 2 года назад

    omg love ur teaching methode . I have learned 10x more from u than my teachers.

  • @user-gl9it3ym4o
    @user-gl9it3ym4o Год назад +1

    There is a small error made,cos placed in place of sin

  • @AbegailAniasco
    @AbegailAniasco 3 месяца назад

    Such a helpful source for learning!

  • @joanad1246
    @joanad1246 7 месяцев назад

    this man has videos on everything, thank you!!!

  • @epicstudios142536
    @epicstudios142536 2 года назад +1

    This channel is elite

  • @user-tr5lu2pf4p
    @user-tr5lu2pf4p 3 года назад +3

    Thank you 😍😍The last stage in high school I hope to get excellent grades 😁from iraq

    • @Ali-cr4zy
      @Ali-cr4zy 2 года назад

      بالتوفيق يا رب يعني طلعت مو بس اني ادور مدرسين اجانب هههههه

  • @jakebyford9804
    @jakebyford9804 3 года назад +3

    @17:00 you say negative cos(2x)'s derivative is negative sin(2x) when it should be positive sin(2x)

    • @katiecastro-tom5204
      @katiecastro-tom5204 2 года назад +2

      Okay I'm glad someone else saw that

    • @vnsalaura3631
      @vnsalaura3631 2 года назад +1

      @@katiecastro-tom5204 me too

    • @Ghostxx
      @Ghostxx 2 года назад

      no its not positive sin, its negative because the derivative of -sin is -cos

  • @refilweramahlo8532
    @refilweramahlo8532 2 года назад +2

    YOU ARE SO AMAZING SIR

  • @yasamandehghan1435
    @yasamandehghan1435 2 года назад +1

    You’re soooo gooood Sir. Thank you so much youre saving me from falling my exams 😂😍

  • @madsgrimholt2904
    @madsgrimholt2904 Год назад +1

    Great video! I was completely stuck on a similar problem to one of these... Thanks dude!

  • @yungifez
    @yungifez 2 года назад +1

    I'm back to your channel again 🤣🤣🤣

  • @IAmNumber4000
    @IAmNumber4000 Год назад +1

    Trigonometric integrals make me wish I was a humble berry picker living 2 million years ago

  • @johnvincentjimar8257
    @johnvincentjimar8257 2 года назад +1

    Thank you so much! I managed to answer my assignment well.

    • @johnvincentjimar8257
      @johnvincentjimar8257 2 года назад +1

      Again, thank you! I just answered my quiz well. This video really helped.

  • @muhesipatrick5074
    @muhesipatrick5074 2 года назад

    You taught me at a good flow rate.this is the best!!

  • @niellyndeklerk2433
    @niellyndeklerk2433 3 года назад

    This guy is an absolute legend!!!!!!!!

  • @chrissilit
    @chrissilit Год назад +1

    thank you very much brother, May God really bless you ,I love your lessons

  • @Algebrainiac
    @Algebrainiac 7 месяцев назад

    9:00 what a coincidence I am having the exact same issue with this problem and I’m working on it rn! Thank you!!

  • @tasneemayham974
    @tasneemayham974 2 года назад +2

    Greetings, Sir!
    I would like to inquire a simple question: how do we decide what is u? In the example you demonstrated as : Find the integral of sin^5x cos^3x. I wanted to make u as cos x. I got -u^4/4 +1/3u^6 - u^8/8. Is that correct? And if it is, why are the answers different?

    • @aadi4272
      @aadi4272 2 года назад +1

      Use LIATE. In this case both are Trigonometric identities so in this case you have to look at what the easier antiderivative is which is cos^3x so you have cosx dv and sin x u. I just started learning calc 2 as well but I always tend to try and find the easier integration. I hope this helps.

    • @JKMath
      @JKMath 2 года назад +1

      @@aadi4272 LIATE doesn't really apply to the particular example Tasneem Ayham is asking about. That trick is commonly used when doing integration by parts and deciding what to make u and dv. LIATE covers all kinds of functions like log functions, exponential functions, etc., when this video is just on trigonometric integrals. I hope that makes sense!

    • @JKMath
      @JKMath 2 года назад +4

      Assuming you are referring to the example at 8:35, (which is sin^5x * cos^2x), deciding what u will be is usually based on what is left after rewriting your integrand with the trig identities. For example, when he gets to the step where he has the integral of (1-cos^2x)^2 * cos^2x * sinx dx, he chose cosx to be u since the derivative of cosx is -sinx and will cancel easily with the remaining sinx in that expression once you plug in du for dx. It is all about rewriting the entire expression in terms of u, and finding how to do so (which may take some trial and error at first, never be afraid to make a mistake when practicing, you will learn from it!) So this is definitely something that takes some practice, but it does get easier to see what to set u equal to as you do more examples. I hope this helps, and keep working at it!

  • @jerrychan4052
    @jerrychan4052 3 года назад +3

    u saved my long weekend🥳🤙🏻

  • @infinityscarf2553
    @infinityscarf2553 2 года назад +1

    When I finish studying Mechanical engineering at university of Nairobi, I shall thank this man. The organic chemistry Tutor.