Integral of sin^4(x)

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  • Опубліковано 20 гру 2024

КОМЕНТАРІ • 263

  • @yadavendrayadav7254
    @yadavendrayadav7254 7 років тому +237

    The best thing about your videos is that you dont skip any steps while explaining. You write every trivial step on the board.
    keep up the good work. All the best

  • @Newbport849
    @Newbport849 9 років тому +494

    Not only is he good at math, he also has a thermal detonator.

    • @no_onecares3266
      @no_onecares3266 4 роки тому +4

      Thermal detonator is only like Mike 🎤but it's shape is only Round

    • @no_onecares3266
      @no_onecares3266 4 роки тому +1

      I can't understand why this comment has 237 likes
      Lol😆😆

    • @no_onecares3266
      @no_onecares3266 4 роки тому

      @@MigueelHoO Are you from which country??

    • @Zahra27756
      @Zahra27756 3 роки тому +1

      @@no_onecares3266 bc a lot of people like me were wondering what that round tech thing is.

    • @no_onecares3266
      @no_onecares3266 3 роки тому

      @@Zahra27756 🖕🖕🖕🖕🖕

  • @nlmaster9811
    @nlmaster9811 6 років тому +114

    If only university professors would explain things half this well.

    • @TheNorgthas
      @TheNorgthas 4 роки тому

      it's pretty common that they are good at experiment and researching but not teaching cause that's not what professors want to concentrate on and they don't take education courses and credits.

    • @foreverknight3448
      @foreverknight3448 3 роки тому +2

      Do they this in Universities really? It's taught in High School in India, perhaps it's a easier question for most indian science student

    • @SohanRazzak
      @SohanRazzak 3 роки тому +6

      @@foreverknight3448 Good For You

    • @Zain69z
      @Zain69z 3 роки тому +1

      This is highschool subject tho...

    • @Zain69z
      @Zain69z 3 роки тому

      @@foreverknight3448 same

  • @tejasvi1775
    @tejasvi1775 2 роки тому +5

    I need such kind of teacher
    RESPECT FROM INDIA🇮🇳

  • @japeking1
    @japeking1 9 років тому +13

    Page 76, Integral 14.350 in Spiegel's Mathematical Handbook. Just as you say. Have you read that sometime in his childhood, Feynman spent most of a summer holiday working out all the integrals in a handbook...without cheating by looking at the solutions first?
    Who would ever have thought that a dumb retired old bloke would get such pleasure from watching and learning integral solving. Thank you.... live long and prosper;-)

    • @SeeingDreams11
      @SeeingDreams11 6 років тому +1

      "Let no corrupt communication proceed out of your mouth, but that which is good to the use of edifying, that it may minister grace unto the hearers." (Blue Letter Bible, KJV, Ephesians 4:29)

  • @Tinyanimalpaws
    @Tinyanimalpaws 4 роки тому +6

    had this on test review, and was stuck! So happy you did this one. Best math youtube channel!!!

  • @alisergio2027
    @alisergio2027 2 роки тому +1

    Thank you, I benefited a lot from you. Greetings of love and respect to you from Iraq 🇮🇶 🧡

  • @ghufranay1586
    @ghufranay1586 5 років тому +1

    I'm from Iraq and your videos are so helpful thank you sooooooooooooooooo much

  • @Asahel717
    @Asahel717 3 роки тому +2

    You’re a great tracher. Thank you for posting such instructive videos.

  • @belmokhtarbentadj9794
    @belmokhtarbentadj9794 8 років тому +3

    you can use this
    1=(sin²(x)+cos²(x
    (cos(2x)=sin²(x) - cos²(x
    and you can somme two equation for reveled more

  • @naveenmadhan593
    @naveenmadhan593 6 років тому +18

    Hey, It would be easier if we use reduction formula....

    • @PKPS01238
      @PKPS01238 6 років тому +4

      Naveen Madhan I have never learned that lol

    • @hilariousharry1890
      @hilariousharry1890 4 роки тому

      @@PKPS01238 you can go and check professor Leonard he has a vid explaining it

    • @yashtripathi9079
      @yashtripathi9079 4 роки тому

      @@PKPS01238 reduction is way easy, you'll pick up fast.

  • @Mrwa24
    @Mrwa24 7 місяців тому

    محد عرف يفهمني غيرك ❤

  • @bonbonpony
    @bonbonpony 8 років тому +1

    02:28 What happened to the binomial formula? It would be shorter to calculate this way...
    But it would be even better to temporarily "hide" the ugly cosines under some 1-letter symbols during simplifying, and back-substitute the cos(2x) later.

  • @random_fact786
    @random_fact786 Рік тому +1

    Still helpful after so long Year🎉

  • @mikuculus3720
    @mikuculus3720 4 роки тому +1

    Awesome video you explain every step flawlessly.

  • @KhushiGupta-gn8gy
    @KhushiGupta-gn8gy 9 місяців тому +1

    Bro your explanation is soo gooddd😭😭😭 every step explained in detailllll 😭😭😭 thanksss bro 😭😭✨✨✨

  • @adityavsx
    @adityavsx 2 місяці тому +1

    have u tried using eulers identity to linearise the sin^4x instead of doing it manually? I find it very helpful in such cases, in this case I think it would be 1/8[cos4x-4cos2x+3]. Well its only just work around. I guess the core remains the same?

    • @adityavsx
      @adityavsx 2 місяці тому

      also I guess I wont be getting an ans cuz its a 9yo comment video

  • @josevalero1230
    @josevalero1230 8 років тому +4

    gracias por la explicación, saludos desde Perú

  • @jameswalker8030
    @jameswalker8030 8 років тому +59

    Why can't my textbook explain it like this :/ Thanks :)

    • @blackpenredpen
      @blackpenredpen  8 років тому +7

      You're welcome

    • @tanushka8678
      @tanushka8678 4 роки тому +7

      Well, in india textbooks can also explain it..😂 usually we use old books thus our seniors have already written a hint of that question or sometimes whole solution :)

  • @renan6827
    @renan6827 4 роки тому

    I wish university professors explain like that. You explained with great details without skip any process. Thank you !!! :-)

    • @no_onecares3266
      @no_onecares3266 4 роки тому

      Renan seriously 🙄!!!
      Bcz in india 12th std. Student can solve this in very easily
      You are University student yet you need explanation ??
      Disgusting

    • @renan6827
      @renan6827 4 роки тому

      @@no_onecares3266 Yeah I should go to India and study math there.

    • @no_onecares3266
      @no_onecares3266 4 роки тому

      @@renan6827 "Atidhi devo bhavah" Most welcome 🙂
      Sister/ brother I teach you definitely

    • @no_onecares3266
      @no_onecares3266 4 роки тому

      @@renan6827 are you girl/boy??

    • @renan6827
      @renan6827 4 роки тому

      @@no_onecares3266 I am a man!!!

  • @dawicool2
    @dawicool2 8 років тому +36

    you explain very fucking well and I love your accent, thank you

    • @blackpenredpen
      @blackpenredpen  8 років тому +41

      Dawich Dawichis thank you f*cking much too!

  • @dineshbommarapu2165
    @dineshbommarapu2165 7 років тому

    bro ur the best maths teacher. keep making more videos

  • @samyo2542
    @samyo2542 4 роки тому

    Thank you from Bangladesh LOVE
    ++++HELPED A LOT ++++++
    SAFIN AHMED

  • @gege1138
    @gege1138 4 роки тому

    Can u explain why we need to use power reduction rule @0:40

  • @vivekgohel5810
    @vivekgohel5810 3 роки тому +1

    Wow sir you're awesome..

  • @holyshit922
    @holyshit922 7 років тому +1

    We can also get reduction formula for this interal using inegration by parts and pythagorean identity

  • @jakec904
    @jakec904 6 років тому

    WAIT, at 3:57 when you're multiplying, shouldn't it be cos(2x)/2 rather than cos(4x)/2? I can't understand the reasoning behind this. Help me please!

    • @anda3487
      @anda3487 6 років тому

      Jake Goykia Power reduction, its cos(2*2x) 4x is correct

  • @pranav_manoj
    @pranav_manoj 4 роки тому

    Yayyyy ! I had fun calculating along with you. Thanks for helping !

  • @onyxtacos3100
    @onyxtacos3100 7 років тому +4

    The intergral For Fonction Sin Et Cos Et Tan its Dificule

  • @aso.211
    @aso.211 Рік тому

    Was struggling with this one, you saved me, that's why I love Asians😞💞💞💞

  • @azadazad3988
    @azadazad3988 5 років тому

    Love from india THANK FOR MAKING SUCH TYPE VIDEO THAT HELP US A LOT

  • @vinodkadu5799
    @vinodkadu5799 4 роки тому

    This question sounds easy. But its actually not. You teach so good. Now I am master in it. LOL🤔🤔🤗🤗

  • @atharvakapade
    @atharvakapade 5 років тому +1

    Really good explanation love it

  • @Jadester
    @Jadester 4 роки тому +1

    So helpful, thank you so much for making these videos

  • @_gossipgirlxoxo
    @_gossipgirlxoxo 5 років тому +1

    The best explanation ever ! Thanks a lot bro 💖

  • @DeepakKumar-pg2en
    @DeepakKumar-pg2en 6 років тому

    I am from india and i loved ur method to solve this

  • @ShubhamKumar-cn1ib
    @ShubhamKumar-cn1ib 6 років тому

    Hey hero...
    Keep going
    You are good at teaching

  • @rairasilva9105
    @rairasilva9105 7 років тому +1

    melhores aulas sempre. valeu !!!

  • @animex2530
    @animex2530 3 роки тому +1

    That's really helps me
    Thanks

  • @jackmiller7324
    @jackmiller7324 2 роки тому

    nice job yo I am doing mat233 worksheet this really helpful

  • @Vegasome
    @Vegasome 8 років тому +4

    omg thank you :D I couldn't get why theres 3x/8 fraction...just now after three hours it hit me thanks to your explanation... omg I'm so dumb lol thanks

  • @gabrielbioletti9010
    @gabrielbioletti9010 7 років тому +1

    You're a great teacher!

  • @Hossam_Elmtbouly
    @Hossam_Elmtbouly 7 років тому

    Your explanation is amazing👏

  • @nychan2939
    @nychan2939 Рік тому

    I've just finished the same problem using integration by parts:
    -sin^3(x)dcos(x)

  • @Jehan696
    @Jehan696 5 місяців тому

    Thank you , brother 🔥❤️

  • @billy1496
    @billy1496 8 років тому +1

    does the same principle apply if ur doing sin^4 (3x) dx ?

    • @AlexR-ATG
      @AlexR-ATG 8 років тому +1

      Yes. Just make sure that when you do the Power Reduction Formula for the first time, that you have cos(6x) instead of cos(2x). When reducing the power, the argument of the trig function doubles.

  • @barsustunel9646
    @barsustunel9646 6 років тому

    thanks man, your videos really helpful.

  • @no_onecares3266
    @no_onecares3266 4 роки тому

    Legend understood whole numerical at 1:23
    I am indian + smart
    That's why I understood this whole numerical within first 3 steps.

  • @wawassake9503
    @wawassake9503 7 років тому

    that was great bro.. thankfull for the answer, it's helpfull. :) keep moving forward :)

  • @payamtaher3996
    @payamtaher3996 3 роки тому

    It is still helpful in 2021

  • @lycheejuicelichigaming2263
    @lycheejuicelichigaming2263 5 років тому

    I did it with your DI method easily by taking sin^x in d side and sinx in i side 😘

  • @anhao5055
    @anhao5055 4 роки тому

    ở bên nước ngoài có học công thức hạ bậc k nhỉ, anh này giảng dễ hiểu quá

  • @elsi-art
    @elsi-art 8 років тому

    Thank you! You saved me wiht my homework

  • @nikhilpratapsingh8790
    @nikhilpratapsingh8790 4 роки тому +1

    Great job

  • @unsunghero1963
    @unsunghero1963 4 роки тому

    Is this the same as hyperbolic function? If i want to integrate sinh⁴(x) and follow this video, the answer is same?

  • @AD-ft8bx
    @AD-ft8bx 9 років тому

    Thank You! This was really helpful!

  • @bradleygahan2405
    @bradleygahan2405 6 років тому

    where does the 1/2 come from infront of 1-cos(x) and why do you have it there for the integral of sin^4 and not there when you integrate sin^3 and sin^5

    • @apostolisvontas
      @apostolisvontas 5 років тому

      Multiplying by 1/2 is like dividing by two so instead of writing the formula (1-cos^2(x))/2 he writes 1/2 · cos^2(x)

  • @kk8490
    @kk8490 5 років тому

    You’re a legend 🙏🏾

  • @OonHan
    @OonHan 7 років тому +4

    Tau - 0:05

  • @takariki1234
    @takariki1234 7 років тому

    I dont understand how u got the 1/2+1/2cos (4x)...please explain

    • @lingmeowww1147
      @lingmeowww1147 7 років тому

      يو آني موسيسي تاريب using half angle formula.

  • @Nish_Poudel
    @Nish_Poudel 11 місяців тому

    What class you are taught this in your country. In my case Nepal it's taught in class 11

  • @rawan4878
    @rawan4878 6 років тому +2

    wew u explain good thanks man

  • @michel_dutch
    @michel_dutch 9 років тому +4

    Nicely explained, thank you! However, you forgot some parentheses on the right side of the whiteboard. Doesn't really matter, it's clear anyway.

  • @juaniththomas3591
    @juaniththomas3591 5 років тому

    Do you refer Indian textbooks for questions? Cause I do see some similarities

  • @badrani6327
    @badrani6327 3 роки тому

    شكرا لك من العراق

  • @johnpaulbdeluna
    @johnpaulbdeluna 7 років тому

    Since i have plans to finish my studies, you review me of integral calculus

  • @MB-zo2xw
    @MB-zo2xw 4 роки тому

    Can we express sin^4(x) as a sum of sin and cos using the complex exponential formulae and then integrate from there?

  • @theroadnottaken_
    @theroadnottaken_ 5 років тому

    thank you! I've been trying this on the online integral calculator but I don't get it. I get it now, thanks to you.

    • @vasunith9682
      @vasunith9682 4 роки тому

      Is that ur real photo in the dp?

    • @theroadnottaken_
      @theroadnottaken_ 4 роки тому

      @@vasunith9682 google Yoo Jeongyeon.

    • @vasunith9682
      @vasunith9682 4 роки тому

      @@theroadnottaken_ okay

    • @vasunith9682
      @vasunith9682 4 роки тому

      Blackpen redpen is korean?

    • @theroadnottaken_
      @theroadnottaken_ 4 роки тому

      @@vasunith9682 I'm not her, but you should definitely check her out. To answer your question, she is indeed korean. Go watch Jeongyeon fancams on youtube! :)

  • @fahimally3923
    @fahimally3923 5 років тому +2

    You should’ve told them about the rule of (a-b)^2=a^2 -2ab+b^2 😇

  • @TroutTruck
    @TroutTruck 3 роки тому

    its crazy how math hasnt changed in 5 years

  • @elonmusk1874
    @elonmusk1874 3 роки тому

    I belongs to India very good sir

  • @fatimaal_zahraa3196
    @fatimaal_zahraa3196 2 роки тому +1

    ماكو طالب سادس من العراق هنانه😂😂😂

  • @joansalazar5884
    @joansalazar5884 5 років тому +1

    Sin este chino no paso el semestre

  • @24x7live_ff
    @24x7live_ff 6 років тому

    Thx sir but can u keep it cam in front of it

  • @arishakiki2441
    @arishakiki2441 5 років тому

    nice channel for learning math

  • @lexinaut
    @lexinaut 8 років тому

    Very nicely presented! 😊 Thanks! The GHOSTS OF DEPARTED QUANTITIES SALUTE YOU! 😊
    The "Ghosts of Departed Quantities" refers to the furious debates regarding infinitesimals in Newton's time and later. It was intended critically, but I think it is a splendid metaphor for differential quantities. And it is said: THE DERIVATIVE DISINTEGRATES THE INTEGRAL! 🌻✨🌟🌻🌈🌎🌝
    Very nicely presented! 😊 Thanks! The GHOSTS OF DEPARTED QUANTITIES SALUTE YOU! 😊
    The "Ghosts of Departed Quantities" refers to the furious debates regarding infinitesimals in Newton's time and later. It was intended critically, but I think it is a splendid metaphor for differential quantities. And it is said: THE DERIVATIVE DISINTEGRATES THE INTEGRAL! 🌻✨🌟🌻🌈🌎🌝

  • @mlfacts7973
    @mlfacts7973 2 роки тому

    nice one mate

  • @pairot01
    @pairot01 9 років тому

    So the power reduction formula is the same for sin and cos? That doesn't seem right

    • @blackpenredpen
      @blackpenredpen  9 років тому

      They are different. For sine is - but for cosine is +

    • @pairot01
      @pairot01 9 років тому

      blackpenredpen Missed that! Makes sense when you think of sin^2(x)+cos^2(x)=1
      Where does the power reduction formula come from?

    • @blackpenredpen
      @blackpenredpen  9 років тому +1

      +Joaquin Pirotto double angle formula for cos(2x)=cos^2x -sin^2x

  • @strangeranjan
    @strangeranjan 3 роки тому +1

    I never thought the answer is solved in like this 😂

  • @BarudeHambisa-z8l
    @BarudeHambisa-z8l 10 місяців тому

    Thank you so much!

  • @nz8380
    @nz8380 7 років тому

    Amazing 😍thaaaaaanx so much ❤

  • @subhashreepanigrahi9263
    @subhashreepanigrahi9263 Рік тому

    Thank you so much sir

  • @daniyalnaqvi2569
    @daniyalnaqvi2569 6 років тому

    Thanks man. Saved me

  • @meinkanal7758
    @meinkanal7758 6 років тому

    Thanks from Algeria

  • @marceliusmartirosianas6104
    @marceliusmartirosianas6104 3 роки тому

    integral of sinx^4 dx= 4 * sinx=[[ 3+ sinx ]=[[ sinx= -3 ] sinx= 3 po versijostada: sinx+cpsx= 1
    statometada turesime : {{ 3+cosx =1 ]=[ cosx=-2 ]=[ po versijos Cosx = 2 ] -2 +3 ]=[1=1 ]
    tda: nulinis laipsyj- sinx+cox=1 sinx=O cosx=1 X= 2pik , pi= 4 , k=1 X= 8 = 2Pi kopernikinis Apskritis , Apskrityje ACADEMIC Marcelius Martirosianas iko Vienas Mire Marcelio mokytojas Algimantas Aksomaitis,Matematikos Destytoja Gyveno Dabar Amerikoje.

  • @tanishqrawat6615
    @tanishqrawat6615 7 років тому

    awesome
    blackpen redpen.......love the name lololololololol

  • @bruvocado
    @bruvocado 2 роки тому

    Genius literally

  • @LK-dn7wm
    @LK-dn7wm 5 років тому

    Thank you SO much

  • @eduardorivera508
    @eduardorivera508 7 років тому

    Can you pleeease make a video explaining something like integral of sin^4(x)cos^2(x) ?

  • @qasim2898
    @qasim2898 4 роки тому

    Thanks from iraq for you

  • @1337ErkaN
    @1337ErkaN 6 років тому

    Why does it not become negative ((sinx)^5)/(5cosx) ?

  • @rachidahlam9636
    @rachidahlam9636 5 років тому

    GOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOD JOB FROM MOROCCO

  • @25.piyushkumarmahtoxiib73
    @25.piyushkumarmahtoxiib73 3 роки тому +1

    using sin^3x.sinx , my answer comes out 4times of what you have.

  • @malekbenhassine3572
    @malekbenhassine3572 5 років тому

    love you

  • @debarpan
    @debarpan 4 роки тому +1

    Rumor has it that he gets all his intelligence from that pokeball of a mic he is holding

  • @morgard211
    @morgard211 6 років тому

    Where did you get that identity? O.o

  • @MeshremMath
    @MeshremMath Рік тому +1

    I was trying to integrate this to find the hyper volume of a 5d sphere embedded in spherical space, and I was struggling hard. The surface of a 5D sphere embedded in spherical space can be measured with ((8)(pi^2)((sin(r))^4)/3)

  • @sheejasuresh9438
    @sheejasuresh9438 4 роки тому

    Gracias brother!!

  • @bijaybera6469
    @bijaybera6469 4 роки тому

    `int(sin4x)/(sin^(4)x)dx`
    What is the solution of this question

  • @cloudanimal5209
    @cloudanimal5209 5 років тому

    Thank you thank you!