Integral of sin^3(x)

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  • เผยแพร่เมื่อ 4 พ.ย. 2024

ความคิดเห็น • 344

  • @altSt0rm
    @altSt0rm 9 ปีที่แล้ว +571

    mesmerised by your pen switching sleight of hand

    • @blackpenredpen
      @blackpenredpen  9 ปีที่แล้ว +54

      This comment made my day!!!

    • @happygarlic13
      @happygarlic13 8 ปีที่แล้ว +3

      +blackpenredpen i strongly sympathise with this comment. and with your sleight of hand. pens for the win!

    • @blackpenredpen
      @blackpenredpen  8 ปีที่แล้ว +8

      +Daniel Walther Thank you, thank you~

    • @blackpenredpen
      @blackpenredpen  7 ปีที่แล้ว +9

      btw, there's a video on that th-cam.com/video/akYITCn0Ecg/w-d-xo.html

    • @handsomepriyansh3424
      @handsomepriyansh3424 ปีที่แล้ว

      Oooo i see...... ❤

  • @david112755
    @david112755 8 ปีที่แล้ว +104

    I appreciate you and your microphone immensely :)

  • @gs_gaming_1361
    @gs_gaming_1361 5 หลายเดือนก่อน +15

    Who's watching this in 2024

  • @saiganesh2001
    @saiganesh2001 5 ปีที่แล้ว +31

    Alternative:
    Use : sin3x=3sinx-4sin³x
    sin³x=(3sinx-sin3x)/4
    ∫ sin³x dx = ∫ (3sinx-sin3x)/4
    on integrating = -(3cosx/4)+cos3x/12

    • @adityasingh5239
      @adityasingh5239 4 ปีที่แล้ว

      👍

    • @raghav9o9
      @raghav9o9 4 ปีที่แล้ว

      But The Answers Are Completely Different How??

    • @saiganesh2001
      @saiganesh2001 4 ปีที่แล้ว +5

      @@raghav9o9 Substitute cos3x =4cos³x - 3cosx. Will be getting the same answer.

    • @alizagurung3406
      @alizagurung3406 2 ปีที่แล้ว +1

      So i am confused can't we use formula of
      Cos2x=1-2sin²x
      sin²x =1-cos2x/2

    • @prakharbajpai3586
      @prakharbajpai3586 2 ปีที่แล้ว +1

      This is exactly what I was done

  • @mikesmate6672
    @mikesmate6672 6 ปีที่แล้ว +137

    In the U world

  • @momozuke2757
    @momozuke2757 4 ปีที่แล้ว +19

    All my classes are online now because of the coronavirus, but these videos are saving me. Thank you bprp 🙏

  • @DanDart
    @DanDart 8 ปีที่แล้ว +170

    I like how this is 3:14

    • @apoolplayer278
      @apoolplayer278 8 ปีที่แล้ว +6

      +Dan Dart 3,14159265358979

    • @apoolplayer278
      @apoolplayer278 8 ปีที่แล้ว +8

      +Dan Dart edit:3.1415926535897932384626432795028841971

    • @bingodeagle
      @bingodeagle 8 ปีที่แล้ว +10

      +a pool player that's wrong after 4626, it goes 46264338327950288419716939937510

    • @michaelkhoo4988
      @michaelkhoo4988 6 ปีที่แล้ว +3

      Taking it up another step 3.14159265358979323846264338327950288419716939937510582097494459230781640628620899

    • @Whatever-sy7hv
      @Whatever-sy7hv 6 ปีที่แล้ว +12

      3.141592653589793238462643383279502884197169399375105820974944592307816406286 208998628034825342117067982148086513282306647093844609550582231725359408128481 117450284102701938521105559644622948954930381964428810975665933446128475648233 786783165271201909145648566923460348610454326648213393607260249141273724587006 606315588174881520920962829254091715364367892590360011330530548820466521384146 951941511609433057270365759591953092186117381932611793105118548074462379962749 567351885752724891227938183011949129833673362440656643086021394946395224737190 702179860943702770539217176293176752384674818467669405132000568127145263560827 785771342757789609173637178721468440901224953430146549585371050792279689258923 542019956112129021960864034418159813629774771309960518707211349999998372978049 951059731732816096318595024459455346908302642522308253344685035261931188171010 003137838752886587533208381420617177669147303598253490428755468731159562863882 353787593751957781857780532171226806613001927876611195909216420198938095257201 065485863278865936153381827968230301952035301852968995773622599413891249721775 283479131515574857242454150695950829533116861727855889075098381754637464939319 25506040

  • @raghunandanbs2005
    @raghunandanbs2005 3 ปีที่แล้ว +1

    Explanation was crystal clear.....
    The way switch the colour of the marker is just cool

  • @saurabhjeena7544
    @saurabhjeena7544 4 ปีที่แล้ว +2

    I love you teaching method ,me from India

  • @diamondsmasher
    @diamondsmasher 8 ปีที่แล้ว +200

    Awesome video. But why are you talking into your shower head?

    • @doogima2491
      @doogima2491 6 ปีที่แล้ว +3

      diamondsmasher ㅋㅋㅋlaughing out loud

    • @kevindiesel6923
      @kevindiesel6923 5 ปีที่แล้ว +2

      lol

  • @alialmahdi4165
    @alialmahdi4165 6 ปีที่แล้ว +8

    Thank you, Asian Ball Man. You've not only helped me remember a missing fragment of the nightmare that was calc II, but you've also taught me to love. To love with the power of the ball.

  • @maanharsingh7414
    @maanharsingh7414 7 ปีที่แล้ว +30

    I love how this video's length is the value of π

  • @user-jw3xj8sv1b
    @user-jw3xj8sv1b ปีที่แล้ว +1

    I'm actually finishing my bachelor engineering, sometimes we forget, but with your video I was back on track, thanks a lot !

  • @happygarlic13
    @happygarlic13 9 ปีที่แล้ว +44

    i like math... seemed more interesting than the rest showing up on youtube.
    this is what i call entertainment while being ill!

  • @Archipelago.
    @Archipelago. 5 ปีที่แล้ว +17

    Sin3x=3sinx - 4sin^3x
    From this formula ,
    Sin^3x=3sinx-sin3x/4
    Now we can easily integrate by taking 1/4 outside and giving integral sign to both of them ...🙂

    • @adityadubey2701
      @adityadubey2701 2 ปีที่แล้ว

      Yes

    • @vishaljuneja1206
      @vishaljuneja1206 2 ปีที่แล้ว +1

      Yes you are completely right but no one ever remembers this formula (at least i never remembered it) though they know about it.What we saw in the video was more "practical" nevertheless whatever people are comfortable with should be used.

    • @alizagurung3406
      @alizagurung3406 2 ปีที่แล้ว

      So i am confused can't we use formula of
      Cos2x=1-2sin²x
      sin²x =1-cos2x/2

  • @digbijoyroy5636
    @digbijoyroy5636 4 ปีที่แล้ว

    sir , you teach so smooth and so clear .

  • @RaginiKumari-xo5cy
    @RaginiKumari-xo5cy 4 ปีที่แล้ว

    Ur talking expressions are totally different from us...but instead of this...it's so helpful..🇮🇳🇮🇳🇮🇳

  • @jane-lyd
    @jane-lyd 9 หลายเดือนก่อน +1

    thank you mate you saved my night

  • @nberz692
    @nberz692 4 ปีที่แล้ว

    Omg. That's the first integral from your channel I solved by myself. Your videos are excellent!

  • @Yoyo-dx8wz
    @Yoyo-dx8wz 5 ปีที่แล้ว +13

    You are really amazing sir. jazakallahu kair. May lord guide u on straight path

  • @divyakantmanguliakr3754
    @divyakantmanguliakr3754 4 ปีที่แล้ว

    Your voice is जबरदस्त... खुप छान...

  • @adityawadikar8842
    @adityawadikar8842 6 ปีที่แล้ว

    You used substitution method nicely.no matter what are you using it matters how are you solving.very great substitution and 5 🌟 for adjusting. By

  • @rTin099
    @rTin099 6 ปีที่แล้ว

    [yet another "thank-you" comment]
    Got here after not understanding the steps my teacher followed to reach the final answer. Awesome video and awesome, super clear explanation. Thanks a lot :)

  • @kimpark1593
    @kimpark1593 3 ปีที่แล้ว

    this one save me so Thank you. I was so clueless about the lesson our instructor send us but through this, now it make sense.

  • @lukschs1
    @lukschs1 5 ปีที่แล้ว +1

    muchas gracias hermano , me suscribo de una . Explicas demasiado bien las integrales

  • @Purple_oceans
    @Purple_oceans 2 ปีที่แล้ว +2

    Your explanation is super to dupper thank you sir . I purple you 💜💜🤩🤩

  • @arkin.g1003
    @arkin.g1003 3 ปีที่แล้ว

    Sir when we use formula. sin³x = 3sinx- sin 3x ÷4 answer is -3÷4cosx+1÷12cos3x +c

  • @mayday4121
    @mayday4121 5 ปีที่แล้ว +1

    Isn't it just sin^4(x)/4cos(x), using the backwards chainrule?
    fx^(n+1)/(n+1)f'x
    Sorry I'm new to this.

  • @krishnavenialagarsamy5616
    @krishnavenialagarsamy5616 4 ปีที่แล้ว

    The pen switching was lit! Thanks so much!

  • @msthicknessMD
    @msthicknessMD 8 ปีที่แล้ว +2

    Great explanation! I could never figure out how to where the negative sign came from. Thanks for the awesome break down!

  • @rindanga4052
    @rindanga4052 8 ปีที่แล้ว

    these all really really help me to understand what's the correct way. thankiee!

  • @wizard.01
    @wizard.01 2 ปีที่แล้ว

    Thankyou! It Helped me to cross check my answer

  • @faisalyousuf7971
    @faisalyousuf7971 3 ปีที่แล้ว

    my o levels are in like few months, and i gotta say, this is actually really helpful bro, thanks for the sweet vid dude

  • @micanal5733
    @micanal5733 7 ปีที่แล้ว

    You make it look easy. Thanks.

  • @kaili3477
    @kaili3477 7 ปีที่แล้ว

    THANK YOU, i have a midterm tmr, and I did not understood substitution properly with trig. This was very helpful!

  • @ZAKI-yg4cg
    @ZAKI-yg4cg 9 วันที่ผ่านมา

    Thank you from 🇩🇿

  • @emmanueldionisio6846
    @emmanueldionisio6846 9 ปีที่แล้ว

    Gracias por la explicación. Are you does videos about series of potential?

  • @ColonizerChan
    @ColonizerChan 5 ปีที่แล้ว +1

    even after taking diff eq and getting past fourier transforms and stuff after that. i still forget things. thank you mate

  • @kondosshabibi67
    @kondosshabibi67 ปีที่แล้ว

    شكرا صاحبي معلم

  • @laiserfish
    @laiserfish 6 หลายเดือนก่อน

    Helpful, I start to forget the most basic trig the higher I go... was trying to use the sin^2x=1/2(1-cos2x) for some reason and thats why I couldn't get it...

  • @somebody-xu4mz
    @somebody-xu4mz 4 ปีที่แล้ว

    I am so grateful for this

  • @ozzim339
    @ozzim339 2 ปีที่แล้ว

    Thank you, saved my homework.

  • @motivationalquotes4239
    @motivationalquotes4239 5 ปีที่แล้ว

    Excellent solution

  • @harikrishnakonakalla4550
    @harikrishnakonakalla4550 5 ปีที่แล้ว

    Superb sir explained superbly

  • @PMundi
    @PMundi 5 ปีที่แล้ว

    Thanks for allowing me to pass calc mate.

  • @LordZanba
    @LordZanba 8 ปีที่แล้ว +1

    I always like videos like this. Furthermore, the video made the process easy to understand. I know this would be a slightly different way of going about solving the integral, but would it not be simpler, using u-substitution, to manipulate du into equaling sinxdx? This would result in -du, which could be plugged back into the integral, then the negative of du (-1 constant) could be brought to the front of the integral.

  • @chinmaydeshmukh9776
    @chinmaydeshmukh9776 5 ปีที่แล้ว +1

    try doing it by coverting it in triple angle. sin3x=3sinx-4sin^3x

  • @maxlarose75
    @maxlarose75 6 ปีที่แล้ว

    It works nicely by parts

  • @japeking1
    @japeking1 9 ปีที่แล้ว +10

    That is lovely. Thank you I feel so daft, 60 years too late to find it all making senseMight as well make this my bucket list... learn another integral....might even try to do some myself before looking to you for the answer.

  • @NitishKumarN30
    @NitishKumarN30 5 ปีที่แล้ว

    I am from India ,really amazing sir

  • @novivi4390
    @novivi4390 7 ปีที่แล้ว

    Thanks a lot i've bees searching for one hour this ^^

  • @vasilibougiamas2958
    @vasilibougiamas2958 6 ปีที่แล้ว +10

    You look very different compared to now.

  • @lexinaut
    @lexinaut 8 ปีที่แล้ว +44

    "U" nailed this nicely, and I am a SUB. (:o)

  • @achrafachbousselham9832
    @achrafachbousselham9832 3 ปีที่แล้ว +1

    The video is π minutes . Perfection 😎👌

  • @ahmmadawshaf
    @ahmmadawshaf 7 ปีที่แล้ว

    Superb tutorial. Thanks a lot man!

  • @whebon7266
    @whebon7266 6 ปีที่แล้ว +8

    Nice video. It's also solvable without substitution (integration by parts):
    ∫ sin^3(x)dx =
    ∫ sin^2(x)sin(x)dx =
    -cos(x)sin^2(x) + 2 ∫ sin(x) cos^2(x)dx
    ∫ sin(x) cos^2(x)dx =
    -cos^3(x) - 2 ∫ sin(x) cos^2(x)dx
    3∫ sin(x) cos^2(x)dx = -cos^3(x)
    ∫ sin(x) cos^2(x)dx = -1/3cos^3(x)
    Plug this back into the original equation:
    ∫ sin^3(x)dx =
    -cos(x)sin^2(x) - 2 * -1/3cos^3(x)=
    -cos(x)sin^2(x) - 2/3cos^3(x)
    So...
    ∫ sin^3(x)dx = -cos(x)sin^2(x) - 2/3cos^3(x)
    Which simplifies to:
    ∫ sin^3(x)dx = -cos(x) + 1/3cos^3(x)

    • @light63478
      @light63478 6 ปีที่แล้ว +4

      Aint no one got time for that

  • @gauravsuyal4456
    @gauravsuyal4456 5 ปีที่แล้ว +8

    Sin3x=3sinx-sin^3x this formula can be used for integration....

    • @RohitShabu
      @RohitShabu 5 ปีที่แล้ว +6

      comedy ka khazana sab ko hasana sin3x= 3sinx-4sin^3x

    • @grandpa8630
      @grandpa8630 4 ปีที่แล้ว

      u r a bit wrong Gaurav
      it should be sin^3(θ)={3sin(θ)−sin(3θ)}/4

  • @christmastubbs2613
    @christmastubbs2613 9 ปีที่แล้ว +1

    Thanks, that was a great refresher.

  • @pedroaragao1754
    @pedroaragao1754 5 ปีที่แล้ว

    Thank you for saving my life. AGAIN!

  • @opclips5715
    @opclips5715 2 ปีที่แล้ว

    But the answer comes out to be -3/4 cosx + 1/12 cos3x + C . By using the identity sin3x = 3sinx - 4sin³x

  • @marymaria3226
    @marymaria3226 6 ปีที่แล้ว

    wow you're amazing teacher thanks a lot

  • @tifnatandmat
    @tifnatandmat 9 ปีที่แล้ว +1

    substitution not necessary, just use integral f'(x)*f(x)^n=(1/(n+1))*f(x)^(n+1)+c

    • @blackpenredpen
      @blackpenredpen  9 ปีที่แล้ว +1

      +tifnatandmat but we didn't have cos(x)
      check this out! th-cam.com/video/kWyzNjjrTBQ/w-d-xo.html

    • @tifnatandmat
      @tifnatandmat 9 ปีที่แล้ว +2

      +blackpenredpen I mean use that when doing the cos^2(x)*sin(x). Your link is the exact rule again, but you did a substitution again. The substitution does the same thing, but is just an extra unnecessary step as this is a reverse chain rule.

    • @blackpenredpen
      @blackpenredpen  9 ปีที่แล้ว +1

      +tifnatandmat Ah I see, you meant the U-substitution part. I thought you meant the trig identity part.

    • @tifnatandmat
      @tifnatandmat 9 ปีที่แล้ว +1

      All good buddy! We're both right :P

    • @blackpenredpen
      @blackpenredpen  9 ปีที่แล้ว +1

      +tifnatandmat yup yup!

  • @marinesreis7219
    @marinesreis7219 8 ปีที่แล้ว

    Thank you!! I was desperate and you helped me a lot!

  • @hannahlorraine4468
    @hannahlorraine4468 4 ปีที่แล้ว

    THANK YOU SO MUCH FOR THIS; V HELPFUL

  • @raghavvishwanath6570
    @raghavvishwanath6570 6 ปีที่แล้ว

    You could also use the formula sin^3x=(3sinx- sin3x)/4

  • @Stekey21
    @Stekey21 8 ปีที่แล้ว

    Very well explained, thank you

  • @kaddourkhineche8436
    @kaddourkhineche8436 6 ปีที่แล้ว

    why u dont use the integral of power function,∫ sin³x dx=1/4(-cos x) sin^4(x) .why

  • @aamirhoda7363
    @aamirhoda7363 6 ปีที่แล้ว

    Wonderfully explained!! 😊😊

  • @azharkhan180
    @azharkhan180 6 ปีที่แล้ว +2

    How to solve if it has double integration and two limits that are 0 to π and 0 to 2π

  • @kamilazdybal
    @kamilazdybal 8 ปีที่แล้ว

    Awesome explanation, thank you!

  • @palomahansen3283
    @palomahansen3283 7 ปีที่แล้ว

    explained it better in 3 minutes than my AP AB Calc teacher did in 50

  • @napow4327
    @napow4327 9 ปีที่แล้ว

    Thanks. This was really helpful!

  • @CYXXYC
    @CYXXYC 8 ปีที่แล้ว +20

    who else was worried at -integral(1-u^2du) where it should be -integral((1-u^2)du)

    • @ahmedhazem6604
      @ahmedhazem6604 7 ปีที่แล้ว

      seriously i spent 5 minutes trying to figure out how he just took out the parentheses!

    • @15october91
      @15october91 7 ปีที่แล้ว +1

      Creative & Random also he forgot +constant after the integration, but then placed it after subbing cosx.

    • @zweiosterei
      @zweiosterei 7 ปีที่แล้ว

      Meeeeeeee

  • @worldvines8462
    @worldvines8462 5 ปีที่แล้ว

    yeah it was really great but is the thing in your hand for translating to english or for recording sound . but i really enjoyed the video so much even subscribed already and also hit the 👍👍👍👍👍👍👍👍👍👍👍👍👍✔

  • @jegorme1ster
    @jegorme1ster 9 ปีที่แล้ว +1

    Danke dir fur es.
    Fantastisch!

  • @yogeshbaisla5885
    @yogeshbaisla5885 6 ปีที่แล้ว +1

    Thanks for solving doubt

  • @LynnXternal
    @LynnXternal 7 ปีที่แล้ว +4

    You can skip a step by distributing the negative sign. Simply flip
    ∫ -(1-u²) du
    like so:
    ∫ u²-1 du

  • @kumaria5244
    @kumaria5244 4 ปีที่แล้ว

    U did it great but I really liked ur baowl

  • @alyaaathirajasmine8716
    @alyaaathirajasmine8716 5 ปีที่แล้ว +1

    omg this came up in my exam the other day

  • @anastasiatimofeeva8184
    @anastasiatimofeeva8184 7 ปีที่แล้ว

    Great job! Thanks a lot! Easy and vivid!

  • @BonjourTube1
    @BonjourTube1 6 ปีที่แล้ว

    Very helpful! Thank you

  • @giovannigioia5217
    @giovannigioia5217 2 ปีที่แล้ว

    Fratè si gruoss!!!! (You're great bro! in Napoletan)

  • @akshayks5109
    @akshayks5109 7 ปีที่แล้ว

    sir ihave opinion that we can directly use du instead of -sinx dx and take the negative sign out of the integral

  • @geetikavirdi3874
    @geetikavirdi3874 6 ปีที่แล้ว

    Thank You. Very well explained. :)

  • @alizagurung3406
    @alizagurung3406 2 ปีที่แล้ว

    So i am confused can't we use formula of
    Cos2x=1-2sin²x
    sin²x =1-cos2x/2

  • @deluxeraliuga5593
    @deluxeraliuga5593 9 ปีที่แล้ว

    thanks me sirvió.. very good !!!

  • @simphiwedlamini.
    @simphiwedlamini. 5 ปีที่แล้ว

    amazees me every time

  • @derimacion2558
    @derimacion2558 8 ปีที่แล้ว

    Awesome video :) , suscribed!

  • @sereykong8756
    @sereykong8756 4 ปีที่แล้ว

    Thank you very much. Teacher

  • @victorgalvez2547
    @victorgalvez2547 5 ปีที่แล้ว

    Me dio gusto resolver este problema sin haber visto la solución.

  • @fraze1228
    @fraze1228 8 ปีที่แล้ว +1

    Error occurs when carrying sin over and cancelling sin x. He should have substituted the sinxdx with -du instead. Although the answer is correct but the way is incorrect which makes will lead to wrong understanding of derivatives.

    • @blackpenredpen
      @blackpenredpen  8 ปีที่แล้ว +1

      +mixeltastic I see what you mean, but the way I do it was sub dx = du/-sinx, which I do have that necessary neg in my steps.

  • @anthealam2474
    @anthealam2474 3 ปีที่แล้ว

    Thank you for your help

  • @nrmlyaroy7135
    @nrmlyaroy7135 4 ปีที่แล้ว +1

    Thank you sir

  • @Darkcreeper555
    @Darkcreeper555 9 ปีที่แล้ว

    Very plain explanation. Good job :)

  • @sivadasanp3006
    @sivadasanp3006 4 ปีที่แล้ว

    Sir what is the integral of ((sinx)^3)/x with limit 0 to infinity?

  • @tezagames56
    @tezagames56 7 ปีที่แล้ว

    Isn't it: -( u - 1/3*U^3 * U) ?
    Because the integral of dU is U so the result should be -(U-1/3*U^4).
    Am I right ? ( don't talk too rich i'm french 😂)

  • @godfather8077
    @godfather8077 2 ปีที่แล้ว

    Thank you alot sir 😊😊😊😊♥️♥️♥️♥️

  • @gobi6546
    @gobi6546 ปีที่แล้ว

    Awesome explanation 🔥🔥🔥

  • @SakanaKuKuRu
    @SakanaKuKuRu 5 ปีที่แล้ว

    I just learnt complex numbers and cams back to look at this vid. Ah how beautiful to see the times where I struggled with integration of weird trigo functions, now with complex numbers it’s almost like cheating.

  • @aaliaank4478
    @aaliaank4478 7 ปีที่แล้ว

    Can you do a video on solving the indefinite integral, from 0 to infinity, sin(x^2) dx or sin^2(x) dx ?