A STUNNING integral from the JEE (main) exam

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  • Опубліковано 31 гру 2024

КОМЕНТАРІ • 54

  • @GiornoYoshikage
    @GiornoYoshikage Рік тому +26

    I've solved it on my own in the same way! Still I admire the used techniques, this was a good integration training!

    • @maths_505
      @maths_505  Рік тому +9

      Yeah it was a fun little exercise but a bit too easy compared to what we do normally on the channel

    • @GiornoYoshikage
      @GiornoYoshikage Рік тому +2

      @@maths_505 Right, usually there's kinda tricky and exciting stuff

    • @maths_505
      @maths_505  Рік тому +3

      @@GiornoYoshikage see ya tomorrow with a number theory problem👻

    • @yassinezanned9837
      @yassinezanned9837 Рік тому

      I did exactly the same thing to solve it 😄

  • @Maths_3.1415
    @Maths_3.1415 Рік тому +4

    ​​@maths_505 bro you are just awesome spreading knowledge around the world through your fascinating integrals

    • @maths_505
      @maths_505  Рік тому

      I once got the chance to see an online integration competition in china.....each and every integral there was an absolute monster!!!

    • @Maths_3.1415
      @Maths_3.1415 Рік тому

      ​@@maths_505 yes, you are true 😅
      Because they do tough mathematics from childhood

  • @aryangadhave1875
    @aryangadhave1875 Рік тому +2

    Alternative: use 2(sin^4x+cos^4x)=1+cos^2(2x) then use u=tan2x

  • @nish5061
    @nish5061 Рік тому +8

    The question is pretty simple and might be one of the easier questions which you discussed on your channel, but believe me brother they look super tough during those 3 hours! But anyways thanks for taking interest in the jee examinations. Do bring more. Love from India❤

    • @maths_505
      @maths_505  Рік тому +2

      With that comment I'll definitely consider posting more of these.
      Thanks bro.

  • @holyshit922
    @holyshit922 Рік тому

    Even and odd decomposition of the function works very well for this example
    f(x)=1/2(f(x)+f(-x))+1/2(f(x)-f(-x))
    1/2(f(x)+f(-x)) is even so we can integrate on interval [0..Pi/4] and double the result
    1/2(f(x)-f(-x)) is odd so integral is zero on interval [-Pi/4..Pi/4]
    I would use u=tan(2x) substitution it gives a little bit better result

  • @niom9446
    @niom9446 Рік тому

    noice, the substitution at the end was cool

  • @lqzlqzlqzlqzlqz
    @lqzlqzlqzlqzlqz Рік тому +1

    What a beautiful integral problem!

  • @MrWael1970
    @MrWael1970 Рік тому

    Smart substitutions. Thank you very much

  • @taterpun6211
    @taterpun6211 Рік тому +7

    Flammy’s technique strikes again

    • @NaN_000
      @NaN_000 Рік тому

      😮

    • @maths_505
      @maths_505  Рік тому +8

      The fundamental theorem of flammy:
      If you have one apple and you take one apple away then you have no apple

  • @linearalgebra2007
    @linearalgebra2007 Рік тому

    This is actually very easy but lengthy
    I think you should do jee advance's 2016's paper 2, 43
    That was one tough bastard

  • @scollyer.tuition
    @scollyer.tuition Рік тому

    The final step with phi looks like some variant of the Cauchy-Schlomilch transformation, I think.

  • @giuseppemalaguti435
    @giuseppemalaguti435 Рік тому

    Intanto (1+e^. ) va via perché al posto di x metto pi/4-pi/4-x...e lavoro un po'... Rimane 1/1-sin2x...alla fine viene integrale da 0 a 1 di 1/(1+t^4)....ovviamente, con le serie, risulta 1-1/5+1/9-1/13+1/17...é sbagliata la integranda 1+t^2/1+t^4.... Ho finalmente rifatto i calcoli.. Pi/2rad2...spero sia giusto, perché non li rifaccio più

  • @pandeyji373
    @pandeyji373 Рік тому +11

    Can you bring questions on topics other than integral, would love a little variety. Love your video btw. Love from India 🇮🇳 ❤❤

    • @maths_505
      @maths_505  Рік тому +7

      Well I do series evaluations and differential equations too so I guess that counts😂
      But yeah I'll add more content soon.

    • @pandeyji373
      @pandeyji373 Рік тому +2

      @@maths_505 Thanks brother 👍
      Your playlists are indeed rich in knowledge.

    • @spiderjerusalem4009
      @spiderjerusalem4009 Рік тому

      number theory & combinatorics 🤔

    • @ThePhysicsParadox
      @ThePhysicsParadox Рік тому

      Pls start integration from basic to advance for clas 12

    • @maths_505
      @maths_505  Рік тому +1

      @@ThePhysicsParadox blackpenredpen's just calculus channel will suffice. My channel isn't exactly a tutoring channel.

  • @bobh6728
    @bobh6728 Рік тому

    4:33 and 6:19 “This is pretty easy”. 9:40 gets the pretty easy answer.

  • @nitroflux_o1040
    @nitroflux_o1040 9 місяців тому

    Got this exam next year... 🙂

  • @autumnleaf6729
    @autumnleaf6729 Рік тому

    Trying JEE Advanced would be fun

  • @shubhamkumar-vx4ld
    @shubhamkumar-vx4ld Рік тому +3

    Please jee advanced also

    • @maths_505
      @maths_505  Рік тому +3

      I did one of those a while back. But these integrals feel like high school integrals solvable with a few tricks. Not exactly the most interesting class of integrals if you ask me.

    • @shubhamkumar-vx4ld
      @shubhamkumar-vx4ld Рік тому +2

      ​@@maths_505 can you suggest me how to improve my integration skills like of yours

    • @maths_505
      @maths_505  Рік тому +5

      @@shubhamkumar-vx4ld just solve as many integrals a day as possible.....it'll all come together pretty neatly.
      Also do series evaluations cuz they're intricately linked with integrals.

  • @utuberaj60
    @utuberaj60 Рік тому +2

    You nailed this one- the key idea being symmetry. Di post such tough integralsas often as you can, from India's toughest exam- JEE Advanced

    • @maths_505
      @maths_505  Рік тому +1

      This one's honestly pretty easy compared to the integrals I normally solve. I've noticed that JEE calculus problems are pretty much high school problems that just need some tricks to get right. Putnam integrals have tricks too but occasionally you find some real gems in the Putnam exam.

    • @iamwhatiam5091
      @iamwhatiam5091 Рік тому

      Indian mathematics Olympiad is much tougher than J.E.E. Advanced. Even I.S.I. (Indian Statistical Institute which is said to be one of the best to get a Math degree from other than Indian Institute of Sciences), I.I.S.E.R. (Indian Institute of Scientific Education and Research) and Chennai Mathematical Institute entrance exams for graduation degrees are very tough.

    • @Whatwillyoudowithmyname
      @Whatwillyoudowithmyname Рік тому +1

      ​@@maths_505Same in JEE You can find some Integral Gems in JEE ADV

    • @Maths_3.1415
      @Maths_3.1415 Рік тому +1

      Jee is tough as lol

  • @rythmx123
    @rythmx123 Рік тому

    well.. taking one bite of the outer side of a candy does not implies it won't have sour flavour in it ;)

  • @ガアラ-h3h
    @ガアラ-h3h Рік тому

    You do it the hard way there a way much easier

  • @vedantpatil8108
    @vedantpatil8108 Рік тому +4

    I am currently preparing for JEE so this wasn't tough for me ...But u must try some JEE ADVANCED integrals

  • @Maths_3.1415
    @Maths_3.1415 Рік тому +4

    Some of the peoples always write JEE is the toughest exam
    ISI, CMI exams in India are way more harder than JEE
    Secondly IMO TST(International mathematical olympiad team selection test) for IMO is the hardest exam in INDIA) with extremely low selection rate only 6 people are selected from 2-2.5 lakh students and this ratio is fixed for last 30 years
    Selection ratio of JEE is 0.0045454545
    Selection ratio of IMO in india is 0.00003
    Selection ratio of IMO in china is 0.0000006
    And Chinese people do JEE math in 9th and 10th grade but they do not show off like you
    Moreover Gaokao of china is toughest engineering exam in the world
    So don't be so obnoxious
    And IMO is for high schoolers below 18 years of age which makes it more difficult than "JEE ADVANCED"
    This is not written for "maths 505"

    • @maths_505
      @maths_505  Рік тому +2

      Dude
      What did I say that sounded obnoxious?

    • @Maths_3.1415
      @Maths_3.1415 Рік тому +2

      ​@@maths_505 I haven't written it for you bro 😂
      It is for those people who are so obnoxious about JEE

    • @Maths_3.1415
      @Maths_3.1415 Рік тому +1

      ​@@maths_505 mene itna sab aapke liye nhi Likha
      Ye unn logon ke liye hai jo Sochte hain ki JEE toughest exam hai

    • @maths_505
      @maths_505  Рік тому

      @@Maths_3.1415 okay but you wrote this as an independent comment rather than a reply to someone else so it sounded like it was for me😂
      It's cool bro....no worries.....nd yes you're right IMOs are pretty tough. Is the Chennai institute the same one that publishes mathematics magazines?

    • @Maths_3.1415
      @Maths_3.1415 Рік тому +1

      ​@@maths_505yes that same one bro