A beautiful trigonometric integral

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  • เผยแพร่เมื่อ 3 ม.ค. 2025

ความคิดเห็น • 38

  • @Jius-fg5zq
    @Jius-fg5zq 3 วันที่ผ่านมา +8

    Hi,
    "Terribly sorry about that": 1:29, 1:57, 3:47, 6:57, 8:54
    "Okaay, cool": 1:47, 11:29, 12:39

  • @kavimahajan8412
    @kavimahajan8412 3 วันที่ผ่านมา +29

    Next thing you know bros gonna be solving a 4th order de

  • @SkEi-y3b
    @SkEi-y3b 3 วันที่ผ่านมา +13

    Seeing our boy Kamal struggling with drawing the [ ] is the best thing in 2025❤❤

  • @CM63_France
    @CM63_France 2 วันที่ผ่านมา +2

    Hi,
    "terribly sorry about that" : 1:30 , 1:57 , 2:00 , 3:47 , 6:58 , 8:56 ,
    "ok, cool" : 1:47 , 4:34 , 7:54 , 11:29 , 12:41 .

  • @andreas_bls
    @andreas_bls วันที่ผ่านมา

    *Happy New Year! Excellent work!*

  • @toadjiang7626
    @toadjiang7626 3 วันที่ผ่านมา

    From about 4:00, you can just use the Mellin transform of ln(1+x) by letting 1/x^2=t and get your final result right away.

  • @orionspur
    @orionspur 3 วันที่ผ่านมา +8

    The suspense over how we get rid of that ⁵√tan is killing me. 😂

  • @bingchilling8384
    @bingchilling8384 3 วันที่ผ่านมา +5

    I wonder if this integral has a general solution for different root values. Maybe you could make a video about it. 🤔

  • @AlexGNR
    @AlexGNR วันที่ผ่านมา

    11:55, wondering if you mixed up the (1-t)^(v-1) and the t^(u-1) here since you got
    f(t) = (1-t)^(-1/10) t^(-9/10)
    Which should be equal to B(u, v) for u-1 = -9/10 and v-1 = -1/10 if I look at the form above
    So B(1/10, 9/10) should be it so exactly the opposite way around as you did, or am I mistaken here and doesnt it matter? I have only barely learned the basics of complex analysis so forgive me if this is wrong

  • @xanterrx9741
    @xanterrx9741 3 วันที่ผ่านมา

    Beautiful result , loved every minute i hope for more videos .

  • @surajrakshit5930
    @surajrakshit5930 3 วันที่ผ่านมา

    Starting the year with a beautiful trig integral nice!

  • @calculusmethods
    @calculusmethods วันที่ผ่านมา

    Nice integral ❤

  • @MrWael1970
    @MrWael1970 3 วันที่ผ่านมา

    Very nice. Thanks

    • @alnfsyh9403
      @alnfsyh9403 3 วันที่ผ่านมา

      يا جنونك يا مستر وائل مينفعش كده

  • @premdeepkhatri1441
    @premdeepkhatri1441 3 วันที่ผ่านมา

    Good method to solve this complicated integration, Thank You for video Kamaal

  • @Nottherealbegula4
    @Nottherealbegula4 3 วันที่ผ่านมา +1

    Terrifying trig integral: Exists
    Bounds being 0 to pi/2: not so terrifying now!

  • @yoav613
    @yoav613 3 วันที่ผ่านมา

    Very nice💯💥

  • @leroyzack265
    @leroyzack265 3 วันที่ผ่านมา +1

    Thanks for this awesome integral that ends the year 2024.

  • @mystery_1101
    @mystery_1101 3 วันที่ผ่านมา

    How can I learn calculus 1, any online resources?

    • @rishabhshah8754
      @rishabhshah8754 3 วันที่ผ่านมา

      3blue1brown's series is quite good for intuition buildig

    • @mystery_1101
      @mystery_1101 3 วันที่ผ่านมา

      @@rishabhshah8754 thanks, i will look into it

    • @divyansh1024
      @divyansh1024 3 วันที่ผ่านมา

      Khan academy

  • @yurfwendforju
    @yurfwendforju 3 วันที่ผ่านมา

    A friend threw this integral at me and I have no idea what to do. The solution isn't very nice he said but maybe one of you fellas wanna try:
    WA doesn't know either.
    I tried to expand the trig functions into their complex definitions but there is not a lot happening still :/
    Integrate [ Cos[ x^2 Log(x) ] / (e^-Sin(x) Sqrt[ Cosh(x) ] ), {x,0,∞} ]

  • @sudhamishra6596
    @sudhamishra6596 3 วันที่ผ่านมา

    Make video on integral includin' the concept of
    Z transformation

  • @LCH0415
    @LCH0415 วันที่ผ่านมา

    Hi bro, I’m a big fan of yours. I really enjoy watching your videos. I have one question for you.
    Um...how can I integrate (ln x)^x dx?? I can't solve it. Plz help me. Thanks

  • @krovraink
    @krovraink 3 วันที่ผ่านมา

    yo I'm kinda new to integration; how do we know that the result using sin²θ will give us 1/2 of the result using sinθ?

    • @Empisee
      @Empisee 3 วันที่ผ่านมา +1

      The power property of logs: log(a^p) = p log(a)

    • @krovraink
      @krovraink 3 วันที่ผ่านมา +1

      @Empisee ohhh right 😭 tysm

  • @hamentaschen
    @hamentaschen 3 วันที่ผ่านมา

    One day center equation results happiness and much positivities. Substantial happiness and durable exponent.

  • @Chiavaccio
    @Chiavaccio 3 วันที่ผ่านมา

    👏👏👏👍

  • @threepointone415
    @threepointone415 3 วันที่ผ่านมา +1

    2025 starting off strong

  • @maxvangulik1988
    @maxvangulik1988 2 วันที่ผ่านมา

    I=1/2•int[0,pi/2](sin^-4/5(Ø)ln(sin(Ø))cos^-6/5(Ø))dØ
    ß(u,v)=2•int[0,pi/2](sin^(2u-1)(Ø)cos^(2v-1)(Ø))dØ
    ðß/ðu=4•int[0,pi/2](sin^(2u-1)(Ø)ln(sin(Ø))cos^(2v-1)(Ø))dØ
    ß(u,v)=Ř(u)Ř(v)/Ř(u+v)
    ðß/ðu=Ř(u)Ř(v)(¥(u)-¥(u+v))/Ř(u+v)
    =(¥(u)-¥(u+v))ß(u,v)
    I=-5pi/4•csc(pi/10)(¥(1/10)-¥(0))/Ř(0)
    not sure if that converges

  • @NurBiswas-fc6ty
    @NurBiswas-fc6ty 3 วันที่ผ่านมา +2

    You should write books on integral calculus and integration,bro.
    Don't waste your talent.

    • @bingchilling8384
      @bingchilling8384 3 วันที่ผ่านมา +7

      I wouldn't say he's wasting his talent. I love his videos, but if he wrote a book i know for sure i wont read it. I just dont really like to read.

    • @Mustafa_Shahzad
      @Mustafa_Shahzad 3 วันที่ผ่านมา +4

      He's making videos, not all teaching talent has to be expressed through books you know

    • @slavinojunepri7648
      @slavinojunepri7648 3 วันที่ผ่านมา +1

      ​@Mustafa_ShahzadVideos is a popular format of reaching teaching very quickly, but books tend to last forever. While the talent isn't wasted on videos, it would be even more beneficial for all if the information was put on books as well.

  • @sudhamishra6596
    @sudhamishra6596 3 วันที่ผ่านมา

    "The Hindu religion is the only one of
    the world's great faiths dedicated to
    the idea that the Cosmos itself
    undergoes an immense, indeed an
    infinite, number of deaths and
    rebirths. It is the only religion in which
    the time scales correspond to those of
    modern scientific cosmology. Its
    cycles run from our ordinary day and
    night to a day and night of Brahma,
    8.64 billion years long. Longer than
    the age of the Earth or the Sun and
    about half the time since the Big
    Bang."
    “Most cultures imagine the world to be a few hundred human generations old. Hardly anyone guessed that the cosmos might be far older but the ancient Hindus did,”
    "It is the only religion in which the time scales correspond, to those of modern scientific cosmology"
    ~ CARL SAGAN (famous astronomer, cosmologist)