Integral of sin^4(x)

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  • Опубліковано 20 вер 2024
  • Integral of sin^4(x) , integral of sin^4x
    solution playlist page www.blackpenred...
    trig integrals, trigonometric integrals, integral of sin(x), integral of tan(x), integral of sec(x), James Stewart single variable Calculus sect 7.2, integration examples, integral examples, antiderivative examples, u substitution examples, integral practice problems, calculus 2 practice problems, blackpenredpen,

КОМЕНТАРІ • 260

  • @yadavendrayadav7254
    @yadavendrayadav7254 6 років тому +228

    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 8 років тому +489

    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

      @@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 5 років тому +113

    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 +1

      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🇮🇳

  • @Tinyanimalpaws
    @Tinyanimalpaws 4 роки тому +6

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

  • @japeking1
    @japeking1 8 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 5 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)

  • @holyshit922
    @holyshit922 6 років тому +18

    We can also get reduction formula from integration by parts and pythagorean identity

  • @dawicool2
    @dawicool2 7 років тому +36

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

    • @blackpenredpen
      @blackpenredpen  7 років тому +41

      Dawich Dawichis thank you f*cking much too!

  • @MeshremMath
    @MeshremMath 9 місяців 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)

  • @KhushiGupta-gn8gy
    @KhushiGupta-gn8gy 6 місяців тому +1

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

  • @jameswalker8030
    @jameswalker8030 7 років тому +59

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

    • @blackpenredpen
      @blackpenredpen  7 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 :)

  • @alisergio2027
    @alisergio2027 2 роки тому +1

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

  • @naveenmadhan593
    @naveenmadhan593 6 років тому +18

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

    • @PKPS01238
      @PKPS01238 5 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.

  • @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

  • @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.

  • @pillowwood
    @pillowwood Рік тому +1

    but if you differentiate the answer you get 1/8cos(4x)-1/2cos(2x)+3/8, how is that (sin(x))^4 ?

  • @mikuculus3720
    @mikuculus3720 4 роки тому +1

    Awesome video you explain every step flawlessly.

  • @ghufranay1586
    @ghufranay1586 5 років тому +1

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

  • @onyxtacos3100
    @onyxtacos3100 7 років тому +4

    The intergral For Fonction Sin Et Cos Et Tan its Dificule

  • @josevalero1230
    @josevalero1230 7 років тому +4

    gracias por la explicación, saludos desde Perú

  • @random_fact786
    @random_fact786 Рік тому +1

    Still helpful after so long Year🎉

  • @samyo2542
    @samyo2542 4 роки тому

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

  • @michel_dutch
    @michel_dutch 8 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.

  • @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!!!

  • @Jadester
    @Jadester 4 роки тому +1

    So helpful, thank you so much for making these videos

  • @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

  • @nychan2939
    @nychan2939 Рік тому

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

  • @vivekgohel5810
    @vivekgohel5810 3 роки тому +1

    Wow sir you're awesome..

  • @_gossipgirlxoxo
    @_gossipgirlxoxo 5 років тому +1

    The best explanation ever ! Thanks a lot bro 💖

  • @pranav_manoj
    @pranav_manoj 4 роки тому

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

  • @Nish_Poudel
    @Nish_Poudel 8 місяців тому

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

  • @dineshbommarapu2165
    @dineshbommarapu2165 7 років тому

    bro ur the best maths teacher. keep making more videos

  • @azadazad3988
    @azadazad3988 4 роки тому

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

  • @atharvakapade
    @atharvakapade 5 років тому +1

    Really good explanation love it

  • @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

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

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

  • @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?

  • @aso.211
    @aso.211 Рік тому

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

  • @rairasilva9105
    @rairasilva9105 7 років тому +1

    melhores aulas sempre. valeu !!!

  • @fahimally3923
    @fahimally3923 5 років тому +2

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

  • @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! 🌻✨🌟🌻🌈🌎🌝

  • @anhao5055
    @anhao5055 4 роки тому

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

  • @billy1496
    @billy1496 8 років тому +1

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

    • @AlexR-ATG
      @AlexR-ATG 7 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.

  • @bijaybera6469
    @bijaybera6469 4 роки тому

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

  • @gabrielbioletti9010
    @gabrielbioletti9010 7 років тому +1

    You're a great teacher!

  • @1337ErkaN
    @1337ErkaN 6 років тому

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

  • @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?

  • @juaniththomas3591
    @juaniththomas3591 5 років тому

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

  • @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)

  • @Hossam_Elmtbouly
    @Hossam_Elmtbouly 7 років тому

    Your explanation is amazing👏

  • @animex2530
    @animex2530 3 роки тому +1

    That's really helps me
    Thanks

  • @Mrwa24
    @Mrwa24 4 місяці тому

    محد عرف يفهمني غيرك ❤

  • @takariki1234
    @takariki1234 7 років тому

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

    • @lingmeowww1147
      @lingmeowww1147 6 років тому

      يو آني موسيسي تاريب using half angle formula.

  • @jackmiller7324
    @jackmiller7324 2 роки тому

    nice job yo I am doing mat233 worksheet this really helpful

  • @Atiya_Siddiqui
    @Atiya_Siddiqui 4 роки тому

    sound problem....it's very low

  • @barsustunel9646
    @barsustunel9646 6 років тому

    thanks man, your videos really helpful.

  • @labib7454
    @labib7454 6 місяців тому

    Bro i got the same answer but my teacher showed me another answer so im confused? The answer was (3x/2 -1/4sin(2x) +1/4sin(4x)+c

  • @vinodkadu5799
    @vinodkadu5799 3 роки тому

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

  • @johnpaulbdeluna
    @johnpaulbdeluna 7 років тому

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

  • @payamtaher3996
    @payamtaher3996 2 роки тому

    It is still helpful in 2021

  • @24x7live_ff
    @24x7live_ff 6 років тому

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

  • @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 😘

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

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

  • @eduardorivera508
    @eduardorivera508 7 років тому

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

  • @mahnoorimranmahnoorimran66
    @mahnoorimranmahnoorimran66 5 років тому

    Plz take limit "0" to "t" and Solve it through convolution theorem

  • @wawassake9503
    @wawassake9503 7 років тому

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

  • @gege1138
    @gege1138 4 роки тому

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

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

    Thank You! This was really helpful!

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

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

  • @rawan4878
    @rawan4878 6 років тому +2

    wew u explain good thanks man

  • @Jehan696
    @Jehan696 2 місяці тому

    Thank you , brother 🔥❤️

  • @pairot01
    @pairot01 8 років тому

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

    • @blackpenredpen
      @blackpenredpen  8 років тому

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

    • @pairot01
      @pairot01 8 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  8 років тому +1

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

  • @elsi-art
    @elsi-art 7 років тому

    Thank you! You saved me wiht my homework

  • @EdgeToFortnite
    @EdgeToFortnite 3 роки тому

    its crazy how math hasnt changed in 5 years

  • @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! :)

  • @mikeljanhajrullaj5784
    @mikeljanhajrullaj5784 5 років тому +2

    dx/(sinx)^4 ??? ...

  • @nikhilpratapsingh8790
    @nikhilpratapsingh8790 4 роки тому +1

    Great job

  • @morgard211
    @morgard211 5 років тому

    Where did you get that identity? O.o

  • @sudhanshubaigra1657
    @sudhanshubaigra1657 7 років тому +1

    Please explain loudly

  • @BarudeHambisa-z8l
    @BarudeHambisa-z8l 7 місяців тому

    Thank you so much!

  • @kk8490
    @kk8490 5 років тому

    You’re a legend 🙏🏾

  • @aluneesan1916
    @aluneesan1916 3 роки тому

    3:26 did he just explained that in his native language

  • @mohammedbelkaidchami680
    @mohammedbelkaidchami680 7 років тому +1

    i need integral 1/1+x^5 and x^x and 1/1-x^7

    • @ernestschoenmakers8181
      @ernestschoenmakers8181 7 років тому

      Use for the 1st and 3rd integral partial fraction decomposition and for the 2nd integral the power of e^ln(x^x).

  • @KaranSingh-ef5gy
    @KaranSingh-ef5gy 4 роки тому

    Integration of sinx is -cosx

  • @antoniomantovani3147
    @antoniomantovani3147 2 роки тому

    - (cosx sinx^3)/4 + 3/4 [- cosx sinx/2 +1/2 x] +c is better

  • @annisaamalias.591
    @annisaamalias.591 5 років тому

    Why dont we use sin²x = 1-cos²x ??

  • @mahnoormalik6118
    @mahnoormalik6118 5 років тому

    What is the Integral of Sin(pi/4) ?
    Please answer I need this urgently. Thank you.

    • @fkncompton7124
      @fkncompton7124 5 років тому

      Sin(pi/4) is a constant, it equals (√2)/2. The integral of (√2)/2 is (√2x)/2

  • @omarchaouch2148
    @omarchaouch2148 9 місяців тому

    my math teacher did it with eulers formula 😢

  • @meinkanal7758
    @meinkanal7758 6 років тому

    Thanks from Algeria

  • @strangeranjan
    @strangeranjan 3 роки тому +1

    I never thought the answer is solved in like this 😂

  • @kaushalgade9238
    @kaushalgade9238 7 років тому

    what is integration of (π-x)^2??????

    • @JustinSuperRulez
      @JustinSuperRulez 7 років тому

      depends on what you're integrating it with respect to

    • @tobi3497
      @tobi3497 7 років тому

      With respect to x, it's ((π-x)^3)/-3
      integral of (ax + b)^n = (ax + b)^(n+1) / ( a*(n+1) )
      Because a (-1) and b (π) are both constant, you can use this formula.
      It only works for linear transformations of x.

  • @elonmusk1874
    @elonmusk1874 2 роки тому

    I belongs to India very good sir

  • @badrani6327
    @badrani6327 3 роки тому

    شكرا لك من العراق

  • @joansalazar5884
    @joansalazar5884 4 роки тому +1

    Sin este chino no paso el semestre

  • @subhashreepanigrahi9263
    @subhashreepanigrahi9263 11 місяців тому

    Thank you so much sir

  • @xristosbart8217
    @xristosbart8217 7 років тому

    you know the power reduction formula (not so useful) and you don't know the this: (a+b)^2 = a^2 + 2ab + b^2 ??

    • @eduardorivera508
      @eduardorivera508 7 років тому +2

      xristos bart He didn't work with (a+b)^2. He worked with (a-b)^2. And he did it correctly.

  • @cloudanimal5209
    @cloudanimal5209 5 років тому

    Thank you thank you!

  • @bruvocado
    @bruvocado 2 роки тому

    Genius literally

  • @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.