integral of x^2/(xsin(x)+cos(x))^2
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- Опубликовано: 16 сен 2018
- A pretty hard integral by integration by parts. Integral of x^2/(x*sin(x)+cos(x))^2,
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#calculus
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wow he solves it in 12 minutes but gives us only 2 seconds to try it.
hahaha : )))
You're supposed to pause the video and try it on your own ~
@@sawmill6358 It's a joke bro
He has to explain it too...😐😐
pause!
We barely get 2 or 3 minutes to solve this problem during exam
So it gets complicated to think like that
When you have already done it is easy
@@ohyeahyeahyeah8396 try solving those 18 questions in an hour and get them all correct 🙂
@@hammer.11011 Bhai, mene bhi mains diya hai. Meri 99.2 percentile hai so pls mujhe pata hai kaise karte hai
@@ohyeahyeahyeah8396 advance ki baat kar Raha hu :)
@@hammer.11011 ye 12th class lvl ka question ha bhai.
Lol, one of my friend ask me the Chinese WiFi problem and I answer immediately pi lolol
LOL
Lol
How many digits though?
Lol
@@ShadicgunMan 6-7 maybe doesn't matter you can solve using 355/113
He never forgets + c .
Quite impressive .
i ALWAYS forget it
My auto correct always adds it
😂😂😂
EXTREMELY impressive
@@dqrksun yo.
tan(x - arctan(x)) + C
1. divide top and bottom by x² so we get 1/(sinx + 1/x * cosx)^2
2. factor out sqrt(1/x^2 + 1) inside the square to get (x^2/(1 + x^2)) * (1/(sinx*1/ sqrt(1/x^2 + 1) + cosx*(1/x)/sqrt(1/x^2 + 1))^2
3. use the formula for cos(a + b) to get (x^2/(1 + x^2)) * sec^2(x - arctan(x))
4. let u = x - arctan(x) so that x^2/(1 + x^2) dx = du, so that the integral becomes integral sec^2 u du
5. Integrate to get tan(x - arctan(x))
WOW!!!!!
@@blackpenredpen sorry I am late but can you explain 3rd line please?
@FolyPlays Expand cos(x-arctan(x)) using cos(a-b)=cosacosb+sinasinb, use cos(arctan(x))=1/sqrt(1+x^2)=1/x*1/(sqrt(1+1/x^2)) and sin(arctan(x))=x/sqrt(1+x^2)=1/sqrt(1/x^2+1)
@@folyplays-getgamified3613 cos(a+b)=cosa cosb-sina sinb
Sure, put it on the exam and hope your students forget about this vodeo/never find it.
Yay
Put on exam integral that i found
Int(x/sqrt(e^{x}+(x+2)^2)dx)
because integral you found is quite easy
Wolfram alpha will not help the students and may lead to wrong conclusions
Integral which i found can be calculated using tricks like adding zero and multiplying by one \
then apply linearity and first will be easy and for second will be easy to find suitable substitution
Int(x/sqrt(e^{x}+(x+2)^2)dx) =
Int((1+(x/sqrt(e^{x}+(x+2)^2)-1))dx)=
Int((1+(x-sqrt(e^{x}+(x+2)^2))/sqrt(e^{x}+(x+2)^2))dx)=
Int(dx)+Int((x-sqrt(e^{x}+(x+2)))/sqrt(e^{x}+(x+2)^2)dx)=
Int(dx)+Int(1/(x+2+sqrt(e^{x}+(x+2)^2))(x+2+sqrt(e^{x}+(x+2)^2)(x-sqrt(e^{x}+(x+2)^2))/sqrt(e^{x}+(x+2)^2))dx)
If we multiply the numerator we will notice that numerator is constant multiple of denominator
blackpenredpen plz solve this question
integral of (xsinx)cosx/sinx + cosx
@@holyshit922 calm down satan
What about int(1/sqrt(x^2+1)) 😁 and without using a formula for int(csc(x))...
90% of views on this video will be from India!
I'm Indian
Am from Tanzania
From india
I'm IIT JEE aspirent
True
Can't wait to slide this to my friend as an easy "Calc. 1" question
#YAY
Sir Rahmed what is calculus 1?
Ankush Singh The first calculus class. Where I took it, “Calc 1” covered derivatives, “Calc 2” was about integration, and “Calc 3” - sometimes called “Multivariable Calculus” - was about applying Calc 1 _and_ Calc 2 to situations involving more than one variable. AFAIK, they’re broken up somewhat similarly across the country (USA for me, dunno about Sir Rahmed) so that it’ll be easier if you need to switch schools. Within reason, of course... you can’t translate classes from a school that uses semesters (about 4 months) to a school that uses quarters (3 months), for example.
Sir Rahmed guess who I found scrolling on the interwebs
@@Capnarchie No way, you watch blackpenredpen too? ;)
Sir Rahmed sometimes
Impossible?
Not with blackpenredpen around.
Actually i calculated it as response of RADHA KUMARI comment two months before blackpenredpen
I had done it in the same way blackpenredpen did
Here we had luck that our numerator cancelled with denominator
and we got easy to calculate inegral
I think that my above example is worth to record video on it
because programs like Wolfram alpha have problems to calculate it and
my way to calculate it may be lost in the other comments
@@holyshit922 integration like this are built up to be cancelled out by ILATE method to integrate further .its not by luck .its the design of such question.thats y integration cannot be done by framing questions ourself
..
ruclips.net/video/y_XwQkchwrE/видео.html
This is possible. and Title is not correct. I have solved this with various methods.
Love these! Your explanations and way of explaining always help me to see clearly the logic and process. So much so that I was able to write the integral down and do it myself from scratch... all the way thru without looking for a hint. And I finished it in around 11 mins. awesome ! Thanks! I find these integrals strangely soothing... :)
Thank you!! : ))))
As a 12th grader studying in India, I can say without a doubt that questions like this are the ones you should be skipping 😂
ruclips.net/video/y_XwQkchwrE/видео.html
Kyu?
Time jayeega. Simpler ones pehle karlo
haha, this is an ncert exemplar question btw💀😭
@@akshatsaini69 it is definitely advanced level
"Let's do some math for fun"
Ummm, don't we always do math for fun?
Math On The Go totally!!!
ruclips.net/video/y_XwQkchwrE/видео.html
I hope my sister will not find your video. 😂😂😂 I will give this as her exercise 😏😏😏.
marlon brade lol, nice!!
Honmestly impressed by the clear explanation and the fact that you went over all the passages.
Also really great attitude
Very cool, and it's great that you explain exactly how you come up with each step. Many teachers don't understand that showing how you think of the solution in the first place is more important than the solution itself.
Thanks for reminding me to subscribe. I had been watching your channel for months and just completely assumed that I had subscribed to you already because I watch your videos so frequently!
DonutKop awww thank you!!!
6:19
bprp: so, we're gonna stop right here...
youtube: *An error occured, please try again later*
I say those are magic pens that know how to do calculus. I want those pens.
Gosh, I love that moment when I'm riding along with the explanation and suddenly something clicks into place! Awesome video!
We did this problem in the 12th class, so...
Of course,I'm from India.
we got the india part from your name.
@@julu2731 so funny hahahahaha.
Stfu
@@julu2731 it's because I liked that game called king of thieves very much.
Yeh this question was for CBSE board eaxm 😂😂 I wonder why he even categorised this question for JEE prep 😂 like what a mockery this is
Come on man I did it in my 10th grade, and I am from the US. Pretty sad you only started it in your 12th.
Integration by parts for quotient. Damn. Clever.
Yay!!
It doesn't sound good. May be you get the answer .
It’s only impossible when more than two pens are required
ruclips.net/video/y_XwQkchwrE/видео.html
I love how his writing gets quicker and more figidty as he approaches his solution. You can see the excitement building! Also, very clever manipulation to be able to intgerate by parts!!!
Apparently everybody is an integration champ from MIT here..
If you wanna boast go somewhere else, this is for the ones who wanna learn.
Yeah you are right.
Yes
Ye sawal 2 ghante me nai bana ..DOUBTNUT NE BHI NAI BATAYA🤣ACHANAK MIL HI GAYAA
Wah
🤣🤣🤣🤣
i did this same problem at my preparation time, really good question to practice . i think the better way to do this is by writing x(square) on numerator as x(square)[sin(square)x + cos(square)x ]
and then solve for it ,i hope it will help you.(it is little bit complex approach but it will open your mind)
or anyways you can always use any suitable method feeling comfortable with.
How........... What are.. The next steps
Maybe some people dislike this video because division by cosx changes the domain
To use another choice for parts we need to manipulate the numerator for example multiply numerator by one (pythagorean)
and add zero to be able to use linearity in the way that in first integral numerator cancels with denominator and second can be integraten by parts but with
different choice of parts
The way you approach problems help me with my maths mainly integrals.
These type of questions come in jee advanced exm which have to be done in 3 to 4 min and this was an easy one.
Keep up the good work
easy if you know the trick.
LIATE (logarithm-inverse trig-algebraic-trig-exponential): a powerful tool but not always the best
We were taught ILATE instead of LIATE.
Isn't it ILATE and not LIATE
Maybe, if you don't mind sounding like the White Rabbit from Alice in Wonderland (-; one pill makes you larger.... ;-)
It's ILATE
we are taught ilate .
Bro you make it a piece of cake great effort here ♥
Yes, great exam question! I came up with a different approach, but this was an easier way to arrive at the solution.
THESE QUESTIONS ARE SUPPOSED TO BE DONE IN 3 4 MINUTES AND WITH THE PRESSURE THAT YOUR FUTURE SOMEWHERE DEPENDS ON THEM... THAT'S WHY NO EXAM CAN BEAT JEE ADVANCE IN TOUGHNESS
😮
Lol look at KVPY it have the most hardest problem in mathematics which are based on not your mathematical skills but how is your scientific approach to mathematics.
Also JEE advance is nothing in front of KVPY
@@raghav9o9 KVPY IS TOO EASY LOOK AT IMO PUTNAM BRO.... BTW I'M IN 10 AND PREPARING FOR JEE AND IMO....
@@msk4246 bro comparing jee it is harder and try to solve question of kvpy also we don't have to fight on this matter we are humans we are here to solve problems not to tell which one is harder every exam has its own level.
@@msk4246 I know putnam is very hard I didn't even try its problem I love mathematics because it tells about the beauty of nature not to pass an exam so stay blessed.
Since the order of the denominator of ○'/○^n decreases and becomes simpler when integrated, it may work well to use it as the integrating side of a partial integration.
I just suscribe to this channel, it brings me memory of my college years...👌
u can also do this ques with substitution : x = tan t...
in denominator u can get the formula of cos ( A-B) and with another sub after it we can get the answer
that was great explanation.thank you
Whenever I see this exam's name all I can think is YEET
Yeah, students get yeeted every year. I am about to be part of that tradition in two days.
Your pronunciation is literally amazing.
You can write xsinx + cosx as one trig
xsinx + cos x = sqrt(x^2+1) cos (x - arctan(x))
Intgeral of (x^2)/(x2+1) × sec^2 ( x-arctanx) dx
Let u = x-arctan(x)
du = (x^2)/(x2+1) dx
Integera of sec^2 (u) du
Answer tan ( x-arctan x ) + C
If you want to get the same answer , you can use the angle difference for tan. Then, replace tanx with sinx/ cosx
This is not even a JEE level question. Even someone like me who is not preparing for JEE can solve this.
JEE questions are much harder than this
I have solved many jee question but this one is tough
@@biswadevmajhi231 for advance, it's moderate level
@@allipse8224 Can you just stop?
@@nathanielhensley4830 It's like the Gaokao or Oxbridge Entrance Exams. Students study specifically for these tests and attend cram schools for years.
@@ichigo449 I know what it is. It's nothing to be proud of.
Love the integral and enjoy your way of teaching ! Always a pleasure to watch and listen ! But this intergral should not be in your calculus 2 EXAM but in a homework that could be evaluated . :D
This video was very helpful. Can you make more videos on IIT JEE advanced tricky questions which will really save some of us
THE WAY U TEACH MAKES THE SUM APPEAR EASY SIR
YOU ARE SUPER AWESOME
I actually solved it by dividing the numerator & denominator by (cosx)^2. Btw, this question was asked in our weekend exam. I'm taking the IIT-JEE exam on May-19-2019.
How did it go?
How did you simplify
ruclips.net/video/y_XwQkchwrE/видео.html
are you alive?
@@karteke Failed to clear the chemistry part ;-;
I did this problem using the ''Harmonic addition theorem'' and I got a slightly different answer.
Watching you is much better than social media tho
Beautiful approach
Hi ,thanks for clearly integral by part. I didn't get this way to integral . I changed xsinx +cosx=cos[x-arctanx] (x^2+1)^(1/2) then this integral has been transformed into X^2/(X^2+1) times sec^2[x-arctanx] ,then I found that d[x-acrtanx]=x^2/(x^2+1) , So I used U substitution , then result is tan(x-arctanx) , I think this is more clear than the wolfram alpha's result .
Hi Bprp,
I wanted to buy two of your “derivatives for you” T-shirt, but I’ve just noticed that the campaign on Teespring.com has ended two days ago, is it correct? What can I do?
Thank you a lot, you’re awesome!
Hi Dottor Gelo,
Yea, it has ended, but I might put it back on again. I am just working somethings out with them at the moment. Sorry.
I never thought that this could be done so smartly
I was new to your channel, so I asked you to try JEE. But you actually did it way before... You are awesome bruhh
Thanks for helping.🙏
Love you💖💖💖💖.
👍👍👍👍👍👍👍👍
Famous problem of JEE ...😂😂
Everyone can solve it
Jee preparators raise their hands from crowd 😂🤣
This was a class 12 problem
🙌
RD Sharma Volume 2
Page 19.132
Example 14
ruclips.net/video/y_XwQkchwrE/видео.html
Wonderful method sir! So much easier and "obvious" once you know the solution (if that made sense)
Thanks for the video. I'mma use this method.
as someone preparing for jee i remember this question as a format of forcing by parts. it was really long but satisfying.
This question came recently in jee main exam which is an entrance exam to just sit in IIT jee exam🙂
Which shift?
@@zynade9334 bro this is forcing integration by parts method
I am not sure which shift but it was in 2020 spetember attempt🙂
(Or january not sure but it was in 2020 mains exam)
@@_AmbujJaiswal Ok thanks, I found it
Great video. Could you please make some videos about teaching some methods instead of explaining problems. That would really help me! Thanks
Another excellent presentation.
No lo habia pensado de esa manera. ¡¡Buen video!!
I've found out a more inquisitive way to solve it.
use harmonic addition theorem on the denominator,and take the argument of the sine function(or cosine,depending on which one you prefer to use) as u,and differentiate.Also you'll have to to an easy partial fraction which immediately follows.
Just try it!
Harmonic addition ?
Is it possible ?
Coefficients in front of trig functions are not constant
Doesn't necessarily have to have constant coefficients.
try to write the denominator as sin(x+arctan(1/x))
then take the argument of this sine function as u and see what happens
How would you even think about that? OMG
Well the denominator looked that much tempting to me to use the harmonic addition PCreeper
That thoerom is not in the syllabus of the exam i think. But if its a good method then good for you!
I'm not gonna lie, I'd probably have missed this question if it was on my calc 2 exam lol
Very ingenious. Congratulation.
Even i have been taught this by my teachers but this explaination cleared my concept thnks sir
I read the description that it was by parts and solved it easily!
Yeah give it in your Calc 2 exam and dont forget to post the students' reaction!!
: )
donitzeti
X sqared means a regular square pattern. Xsinx means multiple waves. cosX added means inverted angles or I. Squaring multiple waves and Angeles ninety means absolute values of waves instances. When you divide one by the other and integrate you get circular ripples.
This is a famous question which came from the coaching modules which use to give it is so easy ❤
Here is my solution:
wolfram alpha the integral. DONE
Oon Han yay!!!
Not in jee syllabus
@@rrr1304 dude issa joke
our teacher did this with 3 methods
Anna Sir
yes! Anna sir!
Sab batana hai is BHARAT ko, xD!
You are incredible bro
Blew my mind, so nice integral
Thanks sir I'm an JEE aspirant. My exam is on 2019.❤Thanks for the video, I'm studying at 3:00 AM this came in my recommendation and helped a lot. Btw which country are you from?
@Sashank Sriram not every asian is chinese bro.😂He can be from Philippines, korea, japan, Vietnam
@@kushagrapandey2466 ...That doesn't mean he's not Chinese though?
My jee exam is on 9 Jan 2019
bprp: It’s actually pretty easy. You just start with a quotient, you differentiate that, and if you see a lot of simplifications it will make the integral really really hard.
me: the derivative of sin(x)/cos(x) simplifies all the way to sec^2(x), therefore it’s really hard
With yoy all is posssible, my respect to you, you are a master in math topics
U know about IIT ? WOWW
@@dr.mikelitoris no u
@@deviprasad_bal I think it's 3rd most difficult exam
@@RC-qi6hs no it's 5th...
1st-CCIE
2nd-GATE
3rd-Gaokao
4th-UPSC
5th-IIT-JEE
@@deviprasad_bal Ty for d correction
@@deviprasad_bal lol out of top 5 difficult Exam 3 exam are of india
It's good w
Question.... I'm from Varanasi India
Have you ever done a video on the Weierstrass substitution method? It's a cool way to simplify lots of trig integrals.
Yes I have.
: )
Yes but he did not finish Euler's substiutions which are closely related to Weierstrass substitution
He did not finish Euler substitution because he showed one but there are three of them
He has also Ostrogradski method for isolation rational part of integral
which may be useful after Weierstrass or Euler substitution
Absolutely beautiful and brilliant
This is basic RD sharma math
Nonsense. Sab ne maths padha hai show-off ke bacche.
Basic nahi hai, advanced hi hai.
@@amj.composer true😂😂
@@amj.composer Kon de class me hai Bhai chota hai Kya 12 me ncert dhang see Ni kri na????
@@Nitro-kx7ok Bhai, hindi nahi aati? Thoda dhang se likhne ki koshish kar. Tere spellings ko dekhke lagta hai ki na tereko English aati hai aur na maa baap ne Hindi sikhayi.
you are way to little of a meaniepus to put this into your exam^^
: )
You could also expand the numerator to x^2sin^2x + x^2cos^2x and simplify.
We are taught this by putting the denominator = t and differentiating. And replacing values its more easy that way but i like the way you make it complex and detailed😃
Damn ! If this was the question the question in last year's cbse board, 80% students of India would've got full marks in this one. 😛
Stop exaggeratating. Boards have way more easier problems. :)
Actually this is one of the easier integrations of iitjee sometimes they ask national mathematics Olympiad level problem those are the main crunch these are the bonus questions that iitians clear
I was sure that you were going to do that haha. Already learned your personality😎
I think similar problem is in grb calculus book and I did it by assuming that answer is f(x)/xsin(x)+cos(x).and differentiating and equating it to the original expression.it was then easy to predict what f(x) could be
I have my IIT JEE exam on January next year 🤪🤪
good luck
it's jee mains? yea?
@@TheRayll yes it's JEE mains
@@TheRayll thanks a lot
@Rahul Pavan yes bro,but widely people know IIT JEE
Khosa.... X (cosx)
Dammit cosine x
Nice train of thought! You could also rewrite xsinx+cosx=sqr(x^2+1)*sin(x+arccotx).
You will see that it perfectly represents the derivative of -cot(f(x)), where f(x)=x+arccotx and f’(x)=x^2/(x^2+1). After integrating, this would yield -cot(x+arccotx)+C.
You are awesome dude!
So its not impossible, ISN'T IT?
ruclips.net/video/y_XwQkchwrE/видео.html
This is so famous and becomes a cakewalk with two substitutions that my teacher pointed out:
x=tan θ
and then (tan θ - θ) = t
you'll get the answer straightway
For integrating by parts try this
FIS-DFIS
(FIRST*INTEGRAL OF SECOND) MINUS (INTEGRAL(DERIVATIVE OF FIRST*INTEGRAL OF SECOND dx))
I was about to try it until I realised it was integrating not differentiating. Not at that stage yet but I’ll be sure to come back in 12 months when I learn it.
This made me unsubscribe just so I could resubscribe for emphasis.
chimetimepaprika Hahahaha aww thank you!
This is not that tough. I asked this question to all of my friends. They were able to do.
Btw I too had cracked JEE Advanced with a rank of 9712 and got admission in Indian Institute of Petroleum and Energy (IIPE), Visakhapatnam.
im gaurav good for you!
@@blackpenredpen
A good reply sir!! But I wasn't trying to show off or anything like that. I just meant this question is okay but not that tough to be called impossible.
Btw you are doing a great work by providing education. I really appreciate it!!
im gaurav well, I put "impossible?" Since I think people would be wondering if that's even possible or not in the first place. So yea.
@@blackpenredpen
Ok. I got it.
Still 'good for you' was a bit rude. It doesn't suit to the educators like you.
And going through all you content, I must say nice work man!
You were trying to show off. Your rank in Jee Advanced cues that it is highly improbable for you to solve such question in first try unless you are familiar with it.
What a coincidence! This question is in our textbook too, and I just did it today and then I get this video 😂
Which rd?
We have a similar question in our Maths book(Cengage)
Only diffn is that in the numerator its x2+20
And its even more tricky!