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❤
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
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
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 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.
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.
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.
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_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?
I've solved it on my own in the same way! Still I admire the used techniques, this was a good integration training!
Yeah it was a fun little exercise but a bit too easy compared to what we do normally on the channel
@@maths_505 Right, usually there's kinda tricky and exciting stuff
@@GiornoYoshikage see ya tomorrow with a number theory problem👻
I did exactly the same thing to solve it 😄
@maths_505 bro you are just awesome spreading knowledge around the world through your fascinating integrals
I once got the chance to see an online integration competition in china.....each and every integral there was an absolute monster!!!
@@maths_505 yes, you are true 😅
Because they do tough mathematics from childhood
Alternative: use 2(sin^4x+cos^4x)=1+cos^2(2x) then use u=tan2x
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❤
With that comment I'll definitely consider posting more of these.
Thanks bro.
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
noice, the substitution at the end was cool
What a beautiful integral problem!
Smart substitutions. Thank you very much
Flammy’s technique strikes again
😮
The fundamental theorem of flammy:
If you have one apple and you take one apple away then you have no apple
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
The final step with phi looks like some variant of the Cauchy-Schlomilch transformation, I think.
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
Can you bring questions on topics other than integral, would love a little variety. Love your video btw. Love from India 🇮🇳 ❤❤
Well I do series evaluations and differential equations too so I guess that counts😂
But yeah I'll add more content soon.
@@maths_505 Thanks brother 👍
Your playlists are indeed rich in knowledge.
number theory & combinatorics 🤔
Pls start integration from basic to advance for clas 12
@@ThePhysicsParadox blackpenredpen's just calculus channel will suffice. My channel isn't exactly a tutoring channel.
4:33 and 6:19 “This is pretty easy”. 9:40 gets the pretty easy answer.
Got this exam next year... 🙂
Trying JEE Advanced would be fun
Please jee advanced also
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.
@@maths_505 can you suggest me how to improve my integration skills like of yours
@@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.
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
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.
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.
@@maths_505Same in JEE You can find some Integral Gems in JEE ADV
Jee is tough as lol
well.. taking one bite of the outer side of a candy does not implies it won't have sour flavour in it ;)
You do it the hard way there a way much easier
I am currently preparing for JEE so this wasn't tough for me ...But u must try some JEE ADVANCED integrals
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"
Dude
What did I say that sounded obnoxious?
@@maths_505 I haven't written it for you bro 😂
It is for those people who are so obnoxious about JEE
@@maths_505 mene itna sab aapke liye nhi Likha
Ye unn logon ke liye hai jo Sochte hain ki JEE toughest exam hai
@@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_505yes that same one bro