❖ Trigonometric Substitution ❖

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  • Опубликовано: 27 окт 2024

Комментарии • 738

  • @misterkmo
    @misterkmo 10 лет назад +273

    I just love how the majority of the examples you do, you do them in permanent marker.....no mistakes, such a beast.

    • @ringo3650
      @ringo3650 9 лет назад +5

      misterkmo
      May be sir just redo everything when he got a slight mistake.

    • @jaimeboston2384
      @jaimeboston2384 3 года назад

      I know im asking the wrong place but does anybody know a tool to log back into an Instagram account?
      I somehow lost my password. I love any assistance you can offer me

    • @jimmyrandy8251
      @jimmyrandy8251 3 года назад

      @Jaime Boston Instablaster =)

    • @jaimeboston2384
      @jaimeboston2384 3 года назад

      @Jimmy Randy Thanks so much for your reply. I got to the site through google and im waiting for the hacking stuff atm.
      Takes quite some time so I will get back to you later with my results.

    • @jaimeboston2384
      @jaimeboston2384 3 года назад

      @Jimmy Randy it did the trick and I now got access to my account again. I'm so happy:D
      Thank you so much, you saved my account!

  • @Peter_1986
    @Peter_1986 10 лет назад +75

    I have learned more about integration from patrickJMT than from my math book, seriously.

  • @patrickjmt
    @patrickjmt  12 лет назад

    @JohnSmith3870 glad to help! and what do you mean: if they ever get taken down with the whole censorship thing...? they are my videos, i keep them here with the help of youtube/google. :)

  • @davidontiveroz8295
    @davidontiveroz8295 10 лет назад +23

    Pat I would venture to say that you have single-handedly affected more future scientists and engineers than any other man in the world with these videos. thanx

  • @patrickjmt
    @patrickjmt  13 лет назад

    @hunterwilbanks donation link on my website ; ) feel free to send as much as you like!

  • @ryanhessong8460
    @ryanhessong8460 6 лет назад +11

    I realize you may not see this comment since the video is so old, but during the summer I took Calculus 1 online and didn't buy the book, because I knew I'd have your videos. This content should not be free and yet it is. It helped me get an A in Calculus 1 and now this semester I am in Calculus 2, I yet again didn't buy the book and am relying on your insightful videos. You help immensely and are the secret to my math success in college. Thank you Patrick.

    • @patrickjmt
      @patrickjmt  6 лет назад +13

      glad i could help!
      and why shouldn't this content be free? :)

  • @BombedNevada
    @BombedNevada 9 лет назад +235

    That moment when patrick JMT drops a sick beat while doing calculus. (12:09)

    • @chaseallbright5658
      @chaseallbright5658 8 лет назад +22

      This made me laugh a little more than it should have.

    • @alexanderwouters3888
      @alexanderwouters3888 8 лет назад +21

      This is the most funny thing I heard today, youre awesome

    • @diy-projects
      @diy-projects 5 лет назад +1

      hahahahaha

    • @buttcracker72
      @buttcracker72 5 лет назад +2

      hahhaha DJ JMT!

    • @s0ndosodn0s
      @s0ndosodn0s 5 лет назад +2

      4 Years later, I'm still laughing at this. I love the internet!

  • @EmoKratiko
    @EmoKratiko 8 лет назад +30

    I can't imagine how many all-nighters I pulled just to watch his videos and understand everything so clearly. It makes calculus so easy cuz of him. :D By the way it's 2:59am RN and still seating on my chair listening to this guy. Thanks for saving my grades!

  • @RedRogue
    @RedRogue 10 лет назад +39

    I cannot express in words how much I love you for this right now.

    • @shadow90004
      @shadow90004 6 лет назад

      RE S I was filled with despair but this video showed me true hope

  • @smexy1856
    @smexy1856 9 лет назад +543

    How many people made this far(Calculus II)? We are absolutely minority.

    • @verahavlicek
      @verahavlicek 9 лет назад +101

      +SMEXY! Nah, man. You're in a minority once you finish diff eqs. and linear algebra.

    • @marcushines4172
      @marcushines4172 9 лет назад +23

      +Victoria Havlicek Abstract Algebra

    • @verahavlicek
      @verahavlicek 9 лет назад +34

      Marcus Hines My point is that you're in a minority once you finish courses that emphasize computation.

    • @aliyuksel9266
      @aliyuksel9266 9 лет назад +43

      +SMEXY! i took calc 1, calc 2, calc 3 and diff eq, then transfered to a diff school, but couldnt get calc 2 to transfer (grade below a c), so im taking it again..one would think its not as hard...but nope..here i am watching these videos...again, and thank you +patrickJMT

    • @twinofny
      @twinofny 8 лет назад +1

      I did up to Linear Algebra and ODE

  • @valcon45
    @valcon45 12 лет назад +2

    You are the only person in my life who explains math in an organized, straightforward, easy to understand way. THANK YOU. My math professor writes on 6 boards maybe 10 times during class and I just give up, but you sir, thank you

  • @patrickjmt
    @patrickjmt  13 лет назад

    @geekgal1000 ya, not everything is on the website ( but most of it should be!)

  • @Tfelde
    @Tfelde 5 лет назад +3

    lol got an ad before that said "are you sick of youtube video from 2006"...why no, no im not. these video's are timeless and absolutely perfect. thanks for helping everyone pass calc 2 for free, keep on keeping on.

    • @mrqueem1703
      @mrqueem1703 5 лет назад

      how do u hear video? mine wont play audio? :x

  • @robmiles2780
    @robmiles2780 8 лет назад +144

    Just wanted to say thank you for doing the Lord's work

    • @patrickjmt
      @patrickjmt  8 лет назад +29

      +Rob Miles jesus, math teacher extraordinaire

    • @JonLG490
      @JonLG490 8 лет назад +5

      +Rob Miles thanks for the laugh

  • @Mrthatguyyouknowable
    @Mrthatguyyouknowable 7 лет назад +6

    I will pass calculus 2 because of you. You're the hero this world needs. Keep doing amazing work

  • @errnita
    @errnita 11 лет назад +84

    Wow, i actually get it now. My professor skipped like 10 million steps during lecture

  • @123killermiller123
    @123killermiller123 9 лет назад +21

    Man I got a Calc 2 exam tomorrow and I think you might have just saved my life!!!

    • @cadencesweetser6907
      @cadencesweetser6907 7 лет назад

      did he save your life

    • @brianhernandez8311
      @brianhernandez8311 7 лет назад +1

      Are you still alive? I got a calc 2 midterm tomorrow aswell

    • @joebilly1907
      @joebilly1907 7 лет назад +13

      No response. Guess he didn't make it...

    • @dwwwwwwwwwwwwwwwwwwwwwww
      @dwwwwwwwwwwwwwwwwwwwwwww 5 лет назад

      Joe Billy they tend to throw curve balls on exams. He should have taken this basic explanation video and applied it to more challenging problems before his exam!

  • @patrickjmt
    @patrickjmt  12 лет назад

    @angelsword1000 you are very welcome

  • @z2zAaronz2z
    @z2zAaronz2z 9 лет назад +1

    It's 1:01 AM right now and I got what I needed from you for my midterm in a 9 hours. Subscribed since 2013 and still going, thanks Patrick.

  • @patrickjmt
    @patrickjmt  13 лет назад

    @Puggalug yep, this is true!

  • @wootenwannabe
    @wootenwannabe 13 лет назад +1

    Once again you've explained something clearly in 14 minutes that a professor couldn't explain in an hour and half of lectures. Not only do you do it in a way that's understandable, you show WHY I'm doing this, my book and professor just assumed I knew that I was factoring the 'a' out. My book doesn't even have the triangle trick. YOU ARE GOD!

  • @tamzidchowdhury472
    @tamzidchowdhury472 4 года назад +2

    God Bless You, I was literally about to cry in the class when my professor was explaining this.

  • @mfm77x38
    @mfm77x38 11 лет назад

    trig substitutions are derived from the right triangle, and in the right triangle if theta is one of the angles then in cosine theta 0

  • @patrickjmt
    @patrickjmt  13 лет назад

    @zloyhimik typically people do not want to see it this way; using the right triangle produces a much more simple equation

  • @patrickjmt
    @patrickjmt  13 лет назад

    @42marthacu glad you like them : )

  • @psford1
    @psford1 12 лет назад

    It never fails me how amazing it is how much easier it is to understand this stuff when this guy teaches it. You truly have a gift. It may as well be a foreign language when my profs teach this!

  • @jmmtcidc
    @jmmtcidc 13 лет назад

    So far this semester, I haven't attended a single lecture for my Calc II class. I watched like 10 of your videos the night before my midterm and I aced it. You are my hero...

  • @TheHunterc12
    @TheHunterc12 8 лет назад

    Love the way you go over examples and show every step. Don't even know why i go to class when my teacher doesn't know how to explain!

  • @songgalackchoi5556
    @songgalackchoi5556 9 лет назад

    I ve watched his video as soon as I `ve had too much trouble with Math. He helped me a lot and he `s better than my teachers ever! Thank you for sharing this awesome video!

  • @TIIJIVIL
    @TIIJIVIL 11 лет назад

    This channel is a blessing from beyond. My math prof comes nowhere close in comparison to your clarity.

  • @MichelLongtin
    @MichelLongtin 13 лет назад

    Really Patrick, you are a blessing, I'm a 65 year old composer who decided to learn calculus; I followed the full 18.01 at MIT and got lost: But with you it is pure poetry a beatiful game and your pedagogy is EXCELLENT, I know I am an emiritus teacher at university of Montreal (music). Thans a thousand times. Michel

  • @patrickjmt
    @patrickjmt  13 лет назад

    @jmmtcidc ha! spread the word about the videos. that is your duty. : )

  • @ryanromigh419
    @ryanromigh419 5 лет назад

    You have outdone 2 weeks of my professor's lectures in 14 minutes and 8 seconds.Thank you for being you

    • @patrickjmt
      @patrickjmt  5 лет назад +1

      glad i could help you out

  • @saravinothini4611
    @saravinothini4611 8 лет назад

    I'm a student from Malaysia and your videos had been extremely helpful . Thank you so much !

  • @dereksellers4361
    @dereksellers4361 9 лет назад

    you sir, are a saint because I cannot understand one thing my professor is doing, and you made it 200x easier! thank you

  • @GloryRainTV
    @GloryRainTV 10 лет назад +151

    "Hallelluyah we have our solution lol"

    • @MarkMcDaniel
      @MarkMcDaniel 6 лет назад +2

      *Hallelujah. A fair misspelling considering it is not a common word.

  • @marlimoller1933
    @marlimoller1933 7 лет назад +1

    So I'm from South Africa and I'm also doing calculus. Since watching your videos after my first test till now, my marks have improved by almost 40%. I am writing a test again this week so I just bought your book (yikes to the Rand/Dollar ratio), but thank you for the great videos and all the help!

  • @patrickjmt
    @patrickjmt  13 лет назад

    @cgsuperpanda1 no problem, happy to help : )

  • @mtoldroyd
    @mtoldroyd 12 лет назад

    Patrick I can't even tell you what a help your videos have been to me. My Calc 2 final is tomorrow, and I'm going back over my practice test, when I come across this trig sub question, but I've totally forgotten how to know which one to use... Then I just look up your trusty videos, and you saved the day again! You're a saint.

  • @TrueDarkness
    @TrueDarkness 13 лет назад

    You're such a good teacher that your videos don't even require sound and I understand them

  • @digit0lchica04
    @digit0lchica04 13 лет назад +1

    My Calc 2 teacher only confuses me more. I really appreciate all the examples. It helps so much with my homework and makes me like math! You should be a college professor if you are not already since you seem to have a gift in explaining complex things.

  • @RECxLESS
    @RECxLESS 12 лет назад

    You're the man. You should have seen the looks on my calc classes' faces when my teacher (who speaks little english) introduced this topic after we were still reeling from trig integrals. Priceless lol, but as always I come to your videos and understand everything. Truly thanks.

  • @MrKingoverall
    @MrKingoverall 6 лет назад

    I love you Patrick. I'm sure you saw this post on another one of your videos, but again I say thank you. You are the reason I graduated man.

  • @patrickjmt
    @patrickjmt  13 лет назад

    @powercrazy11 glad it helped!

  • @Mustang5Speed
    @Mustang5Speed 13 лет назад

    You never fail to help me understand even the most complex problems. You are an excellent teacher. Thank yiu so much for these amazing down to earth and free explanations

  • @babbababbalala46
    @babbababbalala46 7 лет назад

    You go faster than the other videos but not too fast, so at my level, your speed is perfect and thanks for the free math help i am getting of you. Be blessed.

  • @patrickjmt
    @patrickjmt  12 лет назад

    @vanadinite01 no problem, happy to help : )

  • @EE12345
    @EE12345 7 лет назад

    Such a good channel. You explained everything perfectly, no skipping steps but still so concise. Thank you.

  • @rayg5445
    @rayg5445 8 лет назад +12

    i wish you were a professor at my school! I unfortunately have a professor who says "too bad too" sad" if you don't understand the first time around.

    • @JDGWI
      @JDGWI 8 лет назад +1

      Ray G wow

    • @Icecube88
      @Icecube88 7 лет назад +1

      lol

    • @Tony29103
      @Tony29103 6 лет назад +1

      Unfortunately a lot of schools have professors like that. It's sad.

  • @2toasty
    @2toasty 8 лет назад +48

    Wow, I actually understood this, khanacademy and my textbook kept confusing me

    • @patrickjmt
      @patrickjmt  8 лет назад +142

      come here first. my videos are better.

    • @iWinGamer
      @iWinGamer 8 лет назад +9

      patrickJMT we know :)

    • @ldhy1202
      @ldhy1202 7 лет назад +1

      this guy is amazing :v

    • @visionary6498
      @visionary6498 7 лет назад +2

      For real those Khan videos suck lol

    • @StephenCurry-ff4zc
      @StephenCurry-ff4zc 7 лет назад +2

      If khan Academy confuses you, then you probably have a below average IQ. How do u not understand that man? smh

  • @keatonwright5764
    @keatonwright5764 6 лет назад

    i watch your videos for quick refreshers every time I have to tutor someone. I appreciate your videos greatly

  • @patrickjmt
    @patrickjmt  13 лет назад

    @digit0lchica04 thanks for the kind words ; )

  • @user-eo5bh2zg2
    @user-eo5bh2zg2 6 лет назад +1

    Have my Cal 2 final tomorrow. Been binging these videos

  • @patrickjmt
    @patrickjmt  13 лет назад

    @blackhawkdownsnare perfect : )

  • @ebtihal3035
    @ebtihal3035 7 лет назад

    my exam is in 3 hours , i almost gave up on this section, THEN I WATCHED THIS ! it helped me a lot!!! im actually solving problems now! THANKYOU GOD BLESS YOU

  • @MrDapper21
    @MrDapper21 7 лет назад

    6 years later and still the best tutorials i've seen!

  • @faru947
    @faru947 9 лет назад

    Thank you very much ..... U just saved me from screwing up in exams ..... And now I m 100% confident that I can skip my calculus classes and Patrick will save me XD

  • @Kevcom2
    @Kevcom2 13 лет назад +1

    thanks PatrickJMT! Your tutorials are much easier to digest than the material in James Stewart's Calculus Early Transcendentals!

  • @indrit66
    @indrit66 7 лет назад

    How do mathematicans even come up with this.. i have a hard time learning the solution someone found a way to do this from zero. GENIUS!

  • @patrickjmt
    @patrickjmt  13 лет назад

    @pabloMTv ha, nice to see i am missed. i was actually spending some time getting things organized (playlists and stuff) and also working on trying to get some iphone apps out (almost there!). so, i have been doing stuff, just not creating new videos, which is unfortunate, as i hate organizing and like making videos. c'est la vie though, it is stuff that needs to get done!
    hope you are doing well!!

  • @populer208
    @populer208 10 лет назад +25

    "I'm not lazy; I'm efficient" haha

  • @robertjr8205
    @robertjr8205 Год назад

    Needed this to refresh my memory. Taking differential equations next semester and need to re learn integration techniques.

  • @afdelgado1
    @afdelgado1 11 лет назад

    "we are going to use a trig identity thats going to make everything go away"...... you gave me peace when you said that

  • @Monerasauce
    @Monerasauce 12 лет назад

    You're so much neater and more organized than the instructor at the math review I went to today!

  • @patrickjmt
    @patrickjmt  12 лет назад

    @sunnysideup no problem, happy to help :)

  • @patrickjmt
    @patrickjmt  13 лет назад

    @mirzconsulting i did once a long time ago and it was a terrible experience

  • @MritsHunter
    @MritsHunter 10 лет назад

    Even though I have a great calculus teacher I love going to you for your videos. They help solidify the concepts and sometimes help me wrap my head around some concepts. Thank you.

  • @TromboneChamp
    @TromboneChamp 11 лет назад

    I don't think I've said anything about your videos..which if I have then whatever, it needs to be said again. You are amazing; absolutely amazing!!! Do you have a teaching degree by any chance? It just seems like you would because of how talented you are at teaching- your clarity, explanations, and making everything so simple. You're so much better than my Calc professor for sure..who has a Master's in Mathematics, AND a teaching degree

  • @FarrisTX
    @FarrisTX 12 лет назад

    What I meant is, the steps just going through the problem is a lot. Thanks for your tutorial.
    YOU ARE A GENIUS.

  • @tacuachillo4308
    @tacuachillo4308 7 лет назад +13

    Me : hey sis, have you seen a pencil? I'm about to study math.
    Sister : There's a pen right there....why don't you use the pen?
    Me : I'm no patrickJMT, I'm not at that level...

  • @X35max5
    @X35max5 12 лет назад

    This is more then helpful! I am now able to understand the entire concept of these kind of problems... I was so lost in class and you just made it clear... I understand it so perfectly now. Thank you so much! I wish you had an Idea of how much help this is to me!

  • @Tony29103
    @Tony29103 6 лет назад

    As someone who stupidly decided to take Calc 2 online because he knew he'd be working nights and days (on different days each). You have saved my grades. Trying to read my professors notes he posts online, or follow his messed up organizational system is beyond impossible. I'd rather try to do calc 2, while still in middle school then try to follow some of his trains of thought. Whenever I get stuck I come to your videos. (Which has been a lot, especially for trig integrals). Only thing I wish you did more videos on, (maybe it's because it baffles me a bit) is when using washer and shell, I just would have liked more examples. That's it otherwise you are awesome!

  • @Andreas_XD
    @Andreas_XD 9 лет назад +1

    lol finally clarified what i was confused about in the last step…THANK YOU !

  • @killerABcs
    @killerABcs 12 лет назад

    I got it all up to where you have to put theta back into x before watching this video. Now I understand! thanks!

  • @anniemis7120
    @anniemis7120 11 лет назад

    I could never understand my Calc BC class without your help, thank you soo much!

  • @JustAnotherKyd
    @JustAnotherKyd 10 лет назад

    This guy is my favorite math tutor lol. Well done, great video.

  • @Puggalug
    @Puggalug 13 лет назад

    This example actually doesn't necessarily need trigonometric substitution. If you take an x from the x^3 and put it next to the dx (which would make the numerator x^2), you can then use u-substitution.
    Let u = 16 - x^2, x^2 = 16 - u, which means 2x dx = (-1) du, or x dx = (-1/2) du.
    You can then replace the numerator with (16 - u), the denominator with sqrt(u), and the dx with (-1/2) du, and it then becomes the matter of using the reverse power rule after some algebraic manipulation.

  • @Jason-tc8vi
    @Jason-tc8vi 8 лет назад

    Missed class when my professor went over this and you helped me get caught up. Thank you for posting

    • @patrickjmt
      @patrickjmt  8 лет назад

      +Jason McCoid my pleasure! I ha e quite a few of these if you need more

    • @Jason-tc8vi
      @Jason-tc8vi 8 лет назад

      That would be awesome if you could provide links. I'm having trouble with the trig substitution when using x=tan(theta), dx=sec^2(theta)d(theta)... for example, integrate xsqrt(1+x^2)dx. I get the answer: (sec^3(theta))/3) + C, but I'm inclined, since sec = 1/cos, and i found cos to be simply 1, to use 1^3 and can't find any use for the hypotenuse of the triangle where ? = sqrt(x^2 + 1)

    • @Jason-tc8vi
      @Jason-tc8vi 8 лет назад

      Nevermind, dumb pre-cal mistake haha. You showed me what I was doing wrong in your next video. Thanks again

  • @wizzypizzy4813
    @wizzypizzy4813 9 лет назад +29

    Thank you teacher! :)

    • @patrickjmt
      @patrickjmt  9 лет назад +24

      You are very welcome!

    • @pokepokekoi
      @pokepokekoi 8 лет назад +1

      +patrickJMT Your videos are super helpful and easy to follow I'm very grateful for you putting these videos together because they help a ton. Thank you so much!

  • @cinnguyen2192
    @cinnguyen2192 12 лет назад

    I have a quiz tomorrow on this hoping it will help.... I watch your other videos and UR DEF THE BEST TEACHER/WEBSITE ONLINE!! Id say better than KHAN ACADEMY! :D Thanks for putting this up you're seriously the best!

  • @j.deleos1412
    @j.deleos1412 10 лет назад

    Your videos are very helpful. Thanks for all the hard work and for making these videos free.

  • @cgsuperpanda1
    @cgsuperpanda1 13 лет назад

    Going from theta to x is what used to throw me off. I didn't know where to get all my substitution from. One of my friends tried explaining the triangle thing but he used it from the start and that only worked sometimes. D:
    So now I know:
    x to theta: memorize the rules/substitutions
    theta to x: draw the triangle.
    Thank you!! :D

  • @AmayaSkeptic
    @AmayaSkeptic 11 лет назад

    Dude how come you are so Smart? After i finish a course i usually forget most of the material but you are on point.

  • @AvengedRocker92
    @AvengedRocker92 13 лет назад

    Nice Job, Really helped me out with my classwork, and found some new methods of substitution Thankx!

  • @arenasdominic5900
    @arenasdominic5900 5 лет назад

    The hero that nobody asked for but everyone needed.

  • @the_dragons_rage
    @the_dragons_rage 11 лет назад

    started learning this topic this week, goes on this channel to watch a ton of examples and understand, you are the cod(call of duty) god of calc!

  • @UnicornOnTheCob16
    @UnicornOnTheCob16 13 лет назад

    Wow. How convenient. I was just getting ready for a trig sub lab, and this video helped me out big time. You are basically my calc professor

  • @appa37168
    @appa37168 10 лет назад +3

    Hey Patrick, can you do a recap/summary at the end of every tutorial please? That would help a lot.

  • @mrmoonmini
    @mrmoonmini 5 месяцев назад

    really inspiring using substitution by trig it helped me a lot in integration topic

  • @patrickjmt
    @patrickjmt  12 лет назад +3

    i hope the final went well!

  • @barbarax30
    @barbarax30 12 лет назад

    thank you sooooooo much!!!! i had nooo idea how to figure out where the units go on the triangle... my professor always did it as one of the first steps and i was like huh? but doing it later in the problem like you did is sooo much easier to understand! thanks bunches

  • @daniemarie4884
    @daniemarie4884 12 лет назад

    Thank you so much for posting this! I just learned more in 15 minuted from your video than I have in 2 hours of my calc class!!!!!!

  • @KooKL4
    @KooKL4 10 лет назад +4

    You sir are a king.

  • @jacquelinemartinez9523
    @jacquelinemartinez9523 11 лет назад +1

    I wish my professors would teach at the same rate as you do :( they all go way too fast. Your videos always helps, I am very thankful Patrick!

  • @patrickjmt
    @patrickjmt  13 лет назад

    @jsweat2011 this is how i describe it to people

  • @Gixxiemoto
    @Gixxiemoto 12 лет назад

    i never understood the right triangle part until your video,thank you!

  • @blownn420
    @blownn420 4 года назад +1

    Final time. Needed a refresher on these, thanks Patrick! Gonna pass with an A unless I get like a 55% on the final thanks to you ☺️

  • @patrickjmt
    @patrickjmt  11 лет назад

    it is not from beyond; it is from my small little room in austin texas!

  • @DjBeenIt
    @DjBeenIt 12 лет назад

    Work for that youtube money! These videos are a haven for me for exams, thanks man!

  • @patrickjmt
    @patrickjmt  12 лет назад

    there is a ton of stuff missing from my website. it is a nightmare to keep updated