I want all trig functions in one integral!

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  • Опубликовано: 23 дек 2024

Комментарии • 624

  • @blackpenredpen
    @blackpenredpen  Год назад +169

    Learn more calculus on Brilliant: 👉brilliant.org/blackpenredpen/ (now with a 30-day free trial plus 20% off with this link!)

    • @pjshorts4129
      @pjshorts4129 Год назад +3

      Thank you for this information but I really want you to tell some basic for integration thanks you

    • @jonathanv.hoffmann3089
      @jonathanv.hoffmann3089 Год назад +1

      Thanks from Brazil!!!
      🙏♾🎁👏🏻👏🏻👏🏻🎉🎊

    • @mohamedsamsudeen7694
      @mohamedsamsudeen7694 10 месяцев назад

      @blackpenredpen now solve
      Integral
      {[(e power sinx + sqrt(cosx+tanx)] power pi}
      ----------------------------------------
      [ln (ln (cosec x)) + sqrt(sec²x+cot²x)]

    • @dreamdefence7952
      @dreamdefence7952 9 месяцев назад +1

      Nice what is your country name

    • @dreamdefence7952
      @dreamdefence7952 9 месяцев назад +1

      India

  • @JCCyC
    @JCCyC Год назад +2568

    What the student really needs to learn here is not Calculus, but to control their own panic.

    • @CliffSedge-nu5fv
      @CliffSedge-nu5fv Год назад +86

      Exactly! It is natural to feel intimidated and want to reach for the biggest weapon, but this beast can be taken down barehanded.

    • @simonmiller1361
      @simonmiller1361 10 месяцев назад +33

      Biggest thing I realized in calculus is it's not that bad if you master trigonometry

    • @2Blu2
      @2Blu2 9 месяцев назад +10

      Exactly! Like at home sure i have all the time but at the exam I'd feel the cold sweat dripping down my face fr 💀

    • @Scilanze
      @Scilanze Месяц назад

      One professor I had used to tell us that: "in the test we usually put some "ghosts", my recommendation, don't get scare for those "ghosts" at the end they are really easy to deal with"

  • @kalculate1297
    @kalculate1297 Год назад +2129

    i did not expect such a clean solution for this integral

    • @GokuDragon-d4r
      @GokuDragon-d4r Год назад +25

      It was way too easy question though

    • @canyoupoop
      @canyoupoop Год назад +24

      ​@@GokuDragon-d4rayyy same pfp

    • @UKYusei
      @UKYusei Год назад +1

      ​@@canyoupoopwot da fok

    • @goated9415
      @goated9415 Год назад +2

      @@canyoupoop YO LUFFY wyd learning calc bro😭😭😭

    • @mudit2960
      @mudit2960 Год назад

      thats the beauty of math!

  • @fortpile
    @fortpile Год назад +1206

    As a high school cal student, this is, so far, the most satisfying integral I've ever witnessed.

    • @pitoachumi2663
      @pitoachumi2663 Год назад +27

      really?
      come to india baby ull find satisfying triggers everyday then

    • @fortpile
      @fortpile Год назад

      @@pitoachumi2663 oooo

    • @ummmackshually
      @ummmackshually 10 месяцев назад

      ​@@pitoachumi2663or just use the internet

    • @seemaverma7671
      @seemaverma7671 9 месяцев назад

      You better work in your tech support ​@@pitoachumi2663

    • @dhanyajishin8731
      @dhanyajishin8731 7 месяцев назад +5

      @@pitoachumi2663 bro u r so right. I just started calculus and it is already hard. But the truth is this one was extremeley satisfying. But the truth is that in India the most difficult questions would be very easily solved by the teachers but we end up gettting dumbfounded by the same questions. It's annoying but fun.

  • @MichaelZankel
    @MichaelZankel Год назад +4101

    It’s always so funny to me when you add the sin(x)^2 + cos(x)^2 just to make it look harder but it’s just 1 😂 I love it lol

    • @DiverseDose11
      @DiverseDose11 Год назад +70

      If you love physics solve
      The speed of a motor engine decreases from 900 rev/min. to 600rev / min in in 10 seconds. Calculate:
      The angular acceleration
      Number of revolutions made by the motor during this interval
      How many additional seconds are required for motor to come to rest in the same rate

    • @DiverseDose11
      @DiverseDose11 Год назад +26

      If you love physics solve
      find the value of ratio of specific heat capacity for the mixture of gas containing one mole of nitrogen and 2 mole of argon if Gamma of nitrogen is equal to 1.40 and gamma of argon is equal to 1.54

    • @DiverseDose11
      @DiverseDose11 Год назад +19

      If you love physics solve
      3 moles of an ideal gas undergoes a reversible isothermal compression at 27 degree Celsius during this compression 1850 joule of work is done on the gas what is the change in entropy

    • @NiceLol-dl6lq
      @NiceLol-dl6lq Год назад +34

      ​@@DiverseDose11i was literally revising this exact topic ill solve it when i finish revising

    • @DiverseDose11
      @DiverseDose11 Год назад +8

      @@NiceLol-dl6lq yeah it will be nice 👍

  • @General12th
    @General12th Год назад +869

    What a glorious result! I'm going to make this extra credit the first time I teach a calculus class!

    • @blackpenredpen
      @blackpenredpen  Год назад +137

      😆

    • @itachu.
      @itachu. Год назад +2

      Epik

    • @caroot1085
      @caroot1085 10 месяцев назад +17

      All your students who watch blackpenredpen: STONKS!

    • @EvilRamin
      @EvilRamin 6 месяцев назад

      ​@@caroot1085 If they watch this, they deserve the score

  • @Wmann
    @Wmann Год назад +319

    “Everybody’s here”
    I love that part.

  • @gamerpedia1535
    @gamerpedia1535 Год назад +244

    Time to try it out!
    sin²+cos²+tan²=1+tan²=sec²
    (1-2ln(cos))^π
    ln(csc)+ln(sec)+ln(cot)
    = -ln(sin)-ln(cos)+ln(cos)-ln(sin)
    = -ln(sin)
    d/dx(-2ln(sin)) = -2 × cos/sin
    = -2cot
    So the integral becomes
    sin×(1-2ln(cos))^π / -2cos
    u = -ln(cos)
    du = sin/cos dx
    So
    (2u+1)^π du
    Where u = -ln(cos x)
    Now another substitution
    w = 2u+1
    dw = 2du
    So -¼×w^π dw
    Integrates to
    w^π+1 / (-4)(π+1)
    w = 2u+1
    u = -ln(cos x)
    w = 1-2ln(cos x)
    (1-2ln(cos x))^(π+1) / -4(π+1) + C

    • @R8Spike
      @R8Spike Год назад +56

      Lmao it has the translate to english button

    • @mandarbamane4268
      @mandarbamane4268 Год назад +14

      ​@@R8Spike and I got Hindi button &
      sine = sin (pronounced seen) lol

    • @lolynoras-ss8qs
      @lolynoras-ss8qs 8 месяцев назад +2

      why didn't you take the w as 1-2ln(cosx) from the beginning it's easier than two substitutions

    • @TRT_MOOSIC
      @TRT_MOOSIC 6 месяцев назад

      @@mandarbamane4268 for me it was sine = syn

    • @AnuragUpadhyay-s7f
      @AnuragUpadhyay-s7f 5 месяцев назад

      @@TRT_MOOSIC for me it translated sin to "paaap"

  • @MathZeimer
    @MathZeimer Год назад +24

    There is nothing more satisfying than terms that perfectly cancel/match out, leaving a neat answer!

  • @johncraig9310
    @johncraig9310 Год назад +295

    This is the only guy that can make math fun. Keep up the amazing content!

  • @DownDance
    @DownDance Год назад +259

    5:12 My favorite scene because we all know what he means 😂
    This problem was actually quite easy for looking so difficult. The only things I didn't instantly see is the u-sub, because I didn't instantly know the derivative of sec(x)
    Great video!

  • @tomasthemas
    @tomasthemas Год назад +12

    I love how real the problem creation is. Start with a random smattering of operations and functions that look scary then adjust it until a solvable problem appears.

  • @JoseIgnacioZapata
    @JoseIgnacioZapata 10 месяцев назад +3

    You are so calm, smart and good natured I can't help but smile as I watch you solve these. Good work!

  • @nvapisces7011
    @nvapisces7011 Год назад +13

    When i saw this, it sort of look solvable and now i see this being solved makes it so satisfying

  • @MrWaltjam
    @MrWaltjam 9 месяцев назад +5

    as a 50 year old I recently(2020-2022) went back and got my associates degrees after a debilitating health incident that left me reconstructing my base of knowledge. I also wanted to work my brain and ended up taking physics and calculus 1 and 2. At the community college level. I still have memory issues but these videos keep me atleast familiar with the concept of integration. I did well almost coming out with an A but for fractions of points in both.. graduated with a 3.92 gpa. the final Bs in calc I and II got my 4.0.. I can now help my highschool and middleschool children when they get stumped in their advanced math classes.
    I love the depth to which you dive in explaining your process and the sloutions..Your humor is also not lost on me. Fun makes learning more bearable in difficult situations. I only wish my professor was so concerned with teaching the process. After the few example in the book, she assigned out homework. She wanted it the way she taught it but left us to "figure it out" no pun intended.. I would have drowned but for math is power, professor leanard and some of the others. I realized the value of not only knowing but proving the trig identites alittle too late but now I know. I may go back and finish the bachelors in meterology but am leaning toward mathematics just for fun. Keep up the good work, you are opening doors in the minds of many who were traumatized by higher maths as evidenced by the comments.. my only question is whether all the variations of blackpenredpen is actually you? there are several, its hard to tell these days.

  • @ricardomorales213
    @ricardomorales213 Год назад +30

    please make more "insane" looking integrals that are actually fairly easy! I loved the way you break down the solution for something so ridiculous looking :)

  • @RaiymbekZhasulanuly
    @RaiymbekZhasulanuly 12 дней назад +1

    As a person learned basic integration only yesterday, this thing really is fascinating

  • @huwdte
    @huwdte 5 месяцев назад +1

    This integral looks so daunting to complete, and watching it quickly simplify down is just really satisfying

  • @bylightIta
    @bylightIta Год назад +25

    I'm in high school and this year we finally did the indefinite integrals. Now I can comprehend some of this man’s videos. Nice solution

  • @mineapple6726
    @mineapple6726 Год назад +83

    It’s always good when teacher give you things in a test you’ve never seen before, like cscx, secx and cotx

    • @hyacinth5040
      @hyacinth5040 Год назад +10

      True, I love when they teach you the absolute basics and then immediately give you a classwork on the toughest parts without the chance to even study 😀

  • @frogmouth1416
    @frogmouth1416 Год назад +3

    I’m a high school student rn and I’ve been watching blackpenredpen for a few years now. Well I’ve finally made it to calculus in school and this is the first time in my life I’ve actually understood what happened in the vid (normally id just watch and be interested), pretty cool!

  • @Dantido
    @Dantido Год назад +6

    That was just beautiful. I've never seen such a complicated integral become so easy in such a low amount of time.

  • @wistfulgraph
    @wistfulgraph 7 месяцев назад +2

    it feels so blessed to understand this after taking calc bc

  • @qu3nt0r
    @qu3nt0r Год назад +11

    As a student that has no idea what half of those term means, it was enjoyable. I’ll take a look at this again once I learned those terms.

  • @brinoinfantprabu6197
    @brinoinfantprabu6197 Год назад +26

    Your alway best. It seems to be very hard but after your explanation it looks like very easy one. Keep rocking on mathematicians

  • @nomad-1776
    @nomad-1776 6 месяцев назад +1

    I'm just impressed he managed to fit it all on the whiteboard.

  • @Zhinoi
    @Zhinoi Год назад +1

    This is one of the most beautiful integrals I've ever seen...

  • @brunomcleod
    @brunomcleod Год назад +19

    I have not got the faintest idea what he just said, but the way he explained everything made me feel like I did

  • @mcgaming1172
    @mcgaming1172 Год назад +32

    As a 8th grader I understand absolutely nothing but I like the way he is teaching

    • @user-oq7cx2rb4t
      @user-oq7cx2rb4t Год назад

      do you not do calc in year 8 in america?

    • @mcgaming1172
      @mcgaming1172 Год назад

      @@user-oq7cx2rb4t I am not in America, in our country we learn calculus in grade 12 and college

    • @loverofstyanax
      @loverofstyanax Год назад +31

      Bro where do you live that you are doing Calc in year 8?

    • @antiarezzo7630
      @antiarezzo7630 9 месяцев назад

      Instantly assuming he's from the us​@@user-oq7cx2rb4t

    • @marcorizzo3854
      @marcorizzo3854 8 месяцев назад +6

      ​@@R.EDACED6year 8 is like 14 right? Too old for calc 1. Im my country we have math phd by age 16

  • @UtpalAman-tm1tf
    @UtpalAman-tm1tf 9 месяцев назад +1

    Didn't expect such a easy solution

  • @sonictheone4568
    @sonictheone4568 10 месяцев назад

    This was a fun one to do! Cool how all the identities and the u-sub lines up nicely

  • @advayamshud484
    @advayamshud484 Год назад +14

    BlackpenRedpen I really am your fan and i love your videos, your way of explanation fascinates me and I understood every topic of your video, even my mother encourages your teaching and I had watched almost all your videos and I still watch them! Thank you for your teaching and making math enjoyable I had learnt many things from you, and I encourage you to keep going! Al the best!!

  • @lazarussevy2777
    @lazarussevy2777 10 месяцев назад +1

    That was so freaking cool. The best part is that even though it's so complicated, a high schooler should be able to do that if they have taken precalculus and calculus!

  • @johnloman4164
    @johnloman4164 10 дней назад

    This is the most beautiful integral I’ve ever seen

  • @radiantomen5753
    @radiantomen5753 4 месяца назад

    The function becomes undefined every (npi/2, n2pi), and the limit of that function as it goes to kpi+(2pi - pi/2) (where k is an element of odd natural numbers) goes to negative infinity and finding the area from a to b of fx under the curve and a , b are discontinous (like they belong to different sections of graph and are being separated by a discontinuity) will always be -inf so to get a determinate area a,b has to be continous

  • @Cerealdemolisher75
    @Cerealdemolisher75 11 дней назад

    When saw the video where you made the question I actually tried to solve it and it took solid 10 mins before I got the answer.

  • @spikey_sama
    @spikey_sama 4 месяца назад

    The fact that I had to play this video at 2x just gives away how easy that question actually was

  • @RedditChronicles022
    @RedditChronicles022 Год назад +19

    As a grade 12 student myself, I didn't find this too hard. Kinda proud of myself that I am able to do such calculus probelms, with mich ease. Loved the vid.

    • @RJiiFin
      @RJiiFin Год назад

      Well as a grade 11 student myself, I also didn't find this too hard. Kinda weird to flex about that as a grade 12 student though?

    • @RedditChronicles022
      @RedditChronicles022 Год назад

      @@RJiiFin Say whatever you want man, I don't care. I solved the question and I'm proud of it, and no, I don't find it weird to flex about it as a grade 12 student.

    • @RJiiFin
      @RJiiFin Год назад

      @@RedditChronicles022You obviously do care because you responded 😁

    • @RedditChronicles022
      @RedditChronicles022 Год назад +1

      @@RJiiFin Ok well, that's fair. Have a good day tho.

    • @RJiiFin
      @RJiiFin Год назад

      @@RedditChronicles022Thanks, you too! 🙂

  • @federicopagano6590
    @federicopagano6590 Год назад +1

    3:20 thats not true if sin(x) is negative, we were lucky to have ln(cosec(x)) in the denominator

  • @a_man80
    @a_man80 11 месяцев назад +3

    5:46 I thought he is going to say "pi is just 3"

  • @Peter_1986
    @Peter_1986 Год назад +1

    This is the kind of stuff that you throw into Wolfram Alpha when the teachers no longer care about the exact solution steps for integrals.
    That was a really pleasant discovery for me when I started the math courses after calculus, when the teachers started being like "just find the numerical solution in some way".

  • @omurice8534
    @omurice8534 9 месяцев назад

    NO way how did it fit so perfectly

  • @Larsbutb4d
    @Larsbutb4d 6 месяцев назад

    Watching this a month later, where I learnt a bit of diff and int calc, feels so nice to me bc I now understand what these are.

  • @aquss33
    @aquss33 10 месяцев назад

    This is possibly the greatest integral I've ever seen!

  • @anonyone8834
    @anonyone8834 4 месяца назад

    I just know basic trigonometry and nothing about calculus but it was satisfying

  • @om71-m5g
    @om71-m5g 6 месяцев назад

    We completed indefinite integration in our highschool yesterday and first thing in my mind was to visit bprp... And I did solve it on my own before watching his solution. Yay!

  • @saumyacow4435
    @saumyacow4435 Год назад +142

    It's like one of those jokes where you can tell he started with the punchline and worked his way back...
    Problem for students is that if you're stressed out and forget just one of those trig relationships, you're screwed. 😛

    • @avelkm
      @avelkm Год назад +9

      You only need one, sin2+cos2=1 and it can be derived from geometry on the fly. Did that more than once in high school. Trig functions are much easier than some integration tricks and substitutions (the hardest part in this solution frankly)

    • @tombratcher6938
      @tombratcher6938 Год назад

      I guess that's a problem for the student and a reason to git gud foe the teacher...

    • @arulrana4048
      @arulrana4048 Год назад

      @@avelkm doesnt require geometry, just devide by cos^2 or sin^2

    • @prodbygoddi5818
      @prodbygoddi5818 Год назад +3

      @@avelkm to be fair you won't have the time to start deriving some relationships on the fly during a test.

    • @MathsMadeSimple101
      @MathsMadeSimple101 Год назад +1

      He’s high on pot-nuse

  • @NoisterPro
    @NoisterPro 8 месяцев назад +2

    This video is great for revising calculus rather than just fun purposes.

  • @the_aspiring_light
    @the_aspiring_light 5 месяцев назад

    suprisingly ..it was quite easy for me..i hit it right in the first time...nd....glad to see the answer matched ..as a beginner of integration.

  • @FundamSrijan
    @FundamSrijan Год назад +1

    6:18 and where did the chain rule go for sec(x)

  • @uvelergle
    @uvelergle Год назад +1

    Why does -2cotx on the denominator become just -1/2 on the top? What happened to the cotx?
    4:07

    • @square.banana
      @square.banana Год назад

      he rewrote the 1/cotx as tanx in order to bring it to the top :)

    • @uvelergle
      @uvelergle Год назад

      @@square.banana ohh I didn't notice that

  • @peterchege4616
    @peterchege4616 Год назад +11

    Can you do content on partial differential equations (PDEs)

    • @mattreichmann8118
      @mattreichmann8118 Год назад

      They're actually super simple! If you're trying to find the derivative of x^2+y^3+z^4
      Partial derivative of x -- simply treat Y and Z as constants, so you get 2x. That's it!

    • @lazarmendel3784
      @lazarmendel3784 10 месяцев назад

      @@mattreichmann8118 that's not what a pde is

    • @xinpingdonohoe3978
      @xinpingdonohoe3978 10 месяцев назад

      It's not easy. They're very abstract, so methods work for them even less than for regular ODEs.
      I guess one trick is assuming separability, and seeing what transpires.
      So you have a function f(x,y,z). Maybe you're solving something like f_xx=f_yz. Something that looks separable. Just assume f(x,y,z)=X(x)Y(y)Z(z) and see if you can derive a set of solutions.

  • @acloaker600
    @acloaker600 8 месяцев назад

    I love it how brother gets all gitty to do this problem and then starts cranking 90s with the dry-erase marker.

  • @samhess78
    @samhess78 6 месяцев назад

    Best math teacher. You are incredible

  • @Napsap18
    @Napsap18 6 месяцев назад +2

    Don’t forget the plus c!

  • @lukaskamin755
    @lukaskamin755 Год назад +1

    I always feel uncomfortable when even power (2 in this case) is factored in front of ln, while since then the contents of the ln may turn (and we know for sure that it does so in case of trigonometric functions), so strictly speaking you have to put a modulus (abs. value), so that ln (y^2) = 2 ln |y|. But I constatntly see this thing like many alike are neglected while taking integrals, I wonder does it always works? If yes, why, If no, when it works?

  • @jamesd9567
    @jamesd9567 Год назад +4

    This problem rules, and I love that I'm far enough into calculus to be able to not only follow along, but (possibly) solve this type of integral. The only 2 parts I was worried about were taking the derivative of the denominator while leaving it as 2ln|csc|, but it was simple to still get -2cotx. The other part that I'm not sure if I could find is what to set as u, my professor has been very generous with what u is going to equal, but looking back at this problem I would likely originally try setting just secx as u, finding that doesn't work, and then hopefully try setting everything within the parentheses, but we'll see. What strategy would you recommend when trying to find u? I have my exam over this section Tuesday, wish me luck!

    • @jamesd9567
      @jamesd9567 Год назад +1

      Looking back at this with some actual sleep... All this is is a u-sub (and a lot of simplifying) lol. All the trig threw me off since we're doing trig sub and fraction decomp. right now. It's insane that cal 1 could do this, I'm definitely sharing this with my previous professor

    • @沈博智-x5y
      @沈博智-x5y Год назад

      also him not putting absolute values when doing ln(csc^2(x)) = 2ln|csc(x)| = 2ln(csc(x)) is because the integrand restricts csc(x) > 0 by nature
      similarly with ln(sec^2(x))

    • @eshwarthammineni7911
      @eshwarthammineni7911 Год назад

      Coming from a high school student who just learned integration, my teacher recommended I pick an inside function as u, and if the derivative is seen in the expression in the integral, that most likely is u. Again, I might be completely wrong.

    • @沈博智-x5y
      @沈博智-x5y Год назад

      @@eshwarthammineni7911 this generally is a good tactic to try for some integrals.

  • @gocomputing8529
    @gocomputing8529 Год назад +2

    Great video!
    The trick here was to keep the sin in the denominator and the sec in the numerator by playing with the negative exponent

  • @GreenMeansGOF
    @GreenMeansGOF Год назад +5

    This only works if you are in the first quadrant. Otherwise, you need to be careful about pulling the 2’s out of natural log.

    • @沈博智-x5y
      @沈博智-x5y Год назад +3

      but in the original integrand, we have in the denominator ln(csc(x)) ln(sec(x)) etc
      which means it's restricted to first quadrant by nature

  • @Rishith198
    @Rishith198 10 месяцев назад

    This was a very interesting one to solve
    Loved it! :D

  • @yosuakrisnando
    @yosuakrisnando Год назад +1

    🗣️ : "This joke is frankly getting kind of stale"
    Me : "WHAT?!?!" *STONE COLD INTENSIFIES*

  • @JimmyGoodman-u5w
    @JimmyGoodman-u5w Год назад

    I thought you couldn't use the power rule, if the exponent in the log is less than 0. correct me if I'm wrong plz 3:21

  • @smwish6010
    @smwish6010 9 месяцев назад

    It's astonishing that taking calculus can allow me to understand this even a little bit

  • @Kimeters
    @Kimeters Год назад

    love this one, thank you

  • @zihaoooi787
    @zihaoooi787 Год назад +39

    i like how only sec x remains like the others were murdered lol

  • @mani_mincraft
    @mani_mincraft Год назад +5

    Ohh so just add random letters until it’s solved! Just amazing 😭😭😭

  • @Unknown_1096_
    @Unknown_1096_ 11 месяцев назад

    I am pretty sure the product rule uv'+vu' 4:10

  • @marios_-nk4qg
    @marios_-nk4qg 10 месяцев назад

    3:45 isnt the derivative of any constant just 0?

  • @inbaselvangb2006
    @inbaselvangb2006 8 месяцев назад +4

    6:18 Not done the +c 😂😂😂

  • @PimpLink
    @PimpLink 3 месяца назад

    Now do one with all of the trig functions including the inverse and hyperbolic trig functions.

  • @Yossus
    @Yossus Год назад +5

    I love these videos but I have absolutely no idea whether there's a system behind the pen colours or if it's just a semi-random choice thing.

    • @blackpenredpen
      @blackpenredpen  Год назад +6

      It’s systematic. The red is for important parts, new parts or side notes.

  • @gmjackson1456
    @gmjackson1456 Год назад

    Nicely solved!

  • @krypt.shaala
    @krypt.shaala 6 месяцев назад

    I love how there are black and red whiteboard pen boxes in bulk under his table 🥰

  • @iamboomtuber7467
    @iamboomtuber7467 Год назад

    that double tap of pen made me scared, but i mustered courage to face it

  • @peterchege4616
    @peterchege4616 Год назад +2

    Can you explain the vibrating string string 2nd order PDE in a video

  • @CalculusIsFun1
    @CalculusIsFun1 5 месяцев назад

    I got scared for a second and thought it was 1 + (ln(sin^2(x) + cos^2(x) + tan^2(x)))^pi but then i realized it was the whole top raised to pi and a couple trig identities later the answer presented itself.
    Love it.

  • @keirgordon8646
    @keirgordon8646 Год назад +1

    I don't understand any of these but I still watch ur vids

  • @y_auc60seb20
    @y_auc60seb20 Год назад

    This was a beautiful integral

  • @MathFromAlphaToOmega
    @MathFromAlphaToOmega Год назад +7

    Actually, not everybody is here... You forgot hacoversine and covercosine, for example. Those ones always get left out for some reason.

    • @xinpingdonohoe3978
      @xinpingdonohoe3978 Год назад

      You could also include the arctrigonometric functions, the hyperbolic and arhyperbolic functions, even arg or atan2 could come into play.

  • @serae4060
    @serae4060 9 месяцев назад

    I have a question. You use ln(sin(x)^-2)=-2ln(sin(x)). I think this is only valid if sin(x)>=0 but not if sin(x)

  • @DevRaj-my2wo
    @DevRaj-my2wo Год назад

    These are the type of questions which should be left without a thought

  • @revtheobbyist
    @revtheobbyist 9 месяцев назад

    wow its so much easier than i thought

  • @vasco35
    @vasco35 6 месяцев назад

    It turned out really easy

  • @sk3105
    @sk3105 Год назад

    beautifully explained

  • @infinitexgg
    @infinitexgg 6 месяцев назад

    I got everything! nice job

  • @keel28
    @keel28 7 месяцев назад

    I’m too late for this but ever considered adding sinh(x) cosh(x) tanh(x) coth(x) etc, to the integral?

  • @CliffSedge-nu5fv
    @CliffSedge-nu5fv Год назад +1

    Extra Credit: Make lower limit zero and solve for upper limit that makes the definite integral equal to 1.

  • @ANTI_UTTP_FOR_REAL
    @ANTI_UTTP_FOR_REAL Год назад +2

    This came out on my birthday and I didnt even notice it 😂

  • @shipsteer2891
    @shipsteer2891 Год назад

    This looks so hard but is so satisfying

  • @chocholatebunny
    @chocholatebunny Год назад

    Hi, just found your channel, only 1:29 into the video and I can't get past the absolute whiteboard chad moves you're doing with the marker swapping

  • @Zackplayzfriendlol
    @Zackplayzfriendlol Год назад +44

    I like your weird words magic man

  • @brandonfiennies7594
    @brandonfiennies7594 6 месяцев назад +1

    Why not add some hyperbolic trig while you at it

  • @AlumniQuad
    @AlumniQuad Год назад

    6:20 "PLUS C, YAY!"

  • @pitoachumi2663
    @pitoachumi2663 Год назад +2

    maths is all about approach
    everybody can learn fromulae and concepts but approach comes with practice and skills.

  • @EC4U2C_Studioz
    @EC4U2C_Studioz Год назад

    Try doing any integral to the e power.

  • @MemorizadordeVerbos
    @MemorizadordeVerbos 8 месяцев назад +1

    6:20 Where did that +c came from?

    • @Sanatanirohit._
      @Sanatanirohit._ 8 месяцев назад +1

      It's just integral constant

    • @MemorizadordeVerbos
      @MemorizadordeVerbos 8 месяцев назад +1

      @@Sanatanirohit._ IK but why?

    • @user-mo6yo4kz1m
      @user-mo6yo4kz1m 8 месяцев назад +2

      @@MemorizadordeVerbos someone said in comments:
      "it's what you write when you don't have defined bounds for an integral. Given that the derivative of a constant is 0, that means there are an infinite amount of constants that could exist. So we write + C to say "including any constant that was 'lost' due to the derivative of a constant being 0""

    • @xenderman9472
      @xenderman9472 7 месяцев назад +1

      @@MemorizadordeVerboscause if you differentiate it ,you can reach same integration value with any +c or -c ,so it has infinite possibilities,to show that we write +c as a convention (I don’t know wheather convention is right word but yes similar to that)

  • @NeronActivations
    @NeronActivations Год назад

    I have a question regarding trig , why does the cos(x-π/2) = sin(x) but cos(x-90) doesn’t equal sin(x)?

  • @ЄвгенПетренко-щ6п
    @ЄвгенПетренко-щ6п Год назад +7

    Now I know what kind of extra task gonna be solved by my students during their exam tests😁😁😁
    I am good teacher, I am good😝

  • @ZuhaibAhamedMallick
    @ZuhaibAhamedMallick 6 месяцев назад

    I don't know I of integration but it's always fun to watch people solving it 😅

  • @julienmclean6011
    @julienmclean6011 Год назад

    as a math 100 student, can confirm this was on my midterm