In this video, I showed how to integrate the square root of tanx
Пікірлер: 82
@Moj9410 ай бұрын
This is one of those integrals that looks "simple enough" when you're taking an exam.
@jayniesgottagun10 ай бұрын
My God, you're smart and have a gift for teaching. I plan to absorb all you have to give.
@paulstjean859827 күн бұрын
I do enjoy your patience and step by step breakdown. Too bad I'm retired and no longer have students to share this with. Keep it going.
@Jop_pop10 ай бұрын
I've never dived this deep into integrals before and this is probably the most complicated integral ive seen explained so succinctly
@syed33446 ай бұрын
I did it like this: I=int(sqrt(tanx)) Now cosider a new integral J J=int(sqrt(cotx)) I+J=Int.(sqrt(cotx) + sqrt(tanx)) I+J=sqrt(2)*Int.( (sinx+cosx)/sqrt(sin2x)) we know that sin2x = 1-(sinx-cosx)² I+J=sqrt(2)*Int.( (sinx+cosx)/sqrt((1-(sinx-cosx)²) Now substitute sinx+cosx=t (cosx+sinx)dx=dt I+J=sqrt(2)*int.( dt/(sqrt(1-t²)) I+J=sqrt(2)*sin-¹(sinx+cosx)+c1 NOW I-J=Int.(sqrt(cotx) - sqrt(tanx)) I-J=sqrt(2)*Int.( (sinx-cosx)/sqrt(sin2x)) we know that sin2x = (sinx+cosx)²-1 I-J=sqrt(2)*Int.( (sinx-cosx)/sqrt(((sinx+cosx)²-1) Now sinx+cosx=t (cosx-sinx)dx=dt (sinx-cosx)dx=-dt I-J=sqrt(2)*int(-dt/sqrt(t²-1)) J-I=sqrt(2)*int(dt/sqrt(t²-1)) J-I=sqrt(2)*ln|x+sqrt(x²-1)|+ c2 J+I=sqrt(2)*sin-¹(sinx+cosx)+c1 Subtract them -2I= sqrt(2)*[lnx+sqrt(x²-1)-sin-¹(sinx+cosx))+c3
@josephparrish762510 ай бұрын
I love this problem. And, of course, I’ve seen it before. How would a student who has never seen it know what the first move would be? I used to tell my students, “now that you’ve seen me do it, remember the first move!” My students would ask, “how did you know how to do it?” and I would answer, “I saw my professor do it in college!” Lol Anyways, I love your very clear and detailed explanation of a great problem. As always, you amaze with your teaching skills!
@savitrinamdeo-zr5jo9 ай бұрын
Very nice way of explanation nice n clear voice
@bravo29929 ай бұрын
I think our plan was to get rid of root
@Phantom_Reaper_8 ай бұрын
@@bravo2992getting to 2t²/(t⁴+1) is natural enough, but the steps after that just seem too complicated for any student to do in the first time imo
@user-ci9ko7rf7f7 ай бұрын
That's great !!!
@sivasakthisaravanan48505 ай бұрын
There are people who can do it when they see it for the first time, without being taught! But these days as we have Wolfram Alpha, we don't have to manually do any integration😊
@jesusandrade13786 ай бұрын
That form of the final solution is the most simplified and symmetric form, because you can also express the inverse hyperbolic tangent as a logarithm, and yet another form if you use partial fractions after 2t^2/(t^4+1)
@rhm51587 ай бұрын
I used to do this stuff over40 years ago and it’s amazing to me how much I don’t remember. You just blew my mind.
@trivikram49624 күн бұрын
i can finally binge ur videos, as i have just started integration. thanks
@murdock55377 ай бұрын
This is amazing. Many thanks for this awesome "journey".
@PrimeNewtons7 ай бұрын
Glad you enjoyed it!
@cesarmiranda22057 ай бұрын
Outstanding explanation, you are the guy, I really enjoyed, best regards from Brazil.
@paulinofm5 ай бұрын
Maravillosa integral y maravillosa solución. Thanks from Spain. !!!!!
@user-xd8yu4wc5z2 ай бұрын
Keep going your videos are the highlight of my day❤
@Viewpoint3145 ай бұрын
Nice clear writing for this interesting integral.
@NamregSelaur-up4or6 ай бұрын
I solved that integral with two maths skills. 1. Using substitucion. 2. Completing the perfect trinomial.
@saarike4 ай бұрын
Huh, what an integral. Thanks for sharing. Never stop learning or you not living 👍👌👍I have to watch this many times...
@arungosavi56987 ай бұрын
Mind boggling ,sir
@oscarfranciscosantanafranc89486 ай бұрын
You are very smart. God bless you!
@rob8768 ай бұрын
You made a difficult integral look easy.
@user-ti9xi1nt1i10 ай бұрын
Sir you are a genius at mathematics thank you
@servictorovich25768 ай бұрын
однозначно, красивое решение. Достойно похвалы
@maxborn74009 ай бұрын
I remember once in school, one of us wanted to troll the teacher, so we asked, "what is the integral of e^(tan(x))". While it was a joke, I have sometimes wondered about it. Integral of e^(sin(x)) is a Bessel function of order 0. Integral of e^(tan(x)) shows some interesting, convergent properties. But I never get around to formalising it, only numerically studying it. Would be interesting if we could some day find an analytical expression for that, or just a "special functions" recursive series (I think I have that somewhere).
@user-ug3vn2mj7t8 ай бұрын
Good math go head for more thank you man 👍👍👍
@joelmacinnes23914 ай бұрын
I knew that the integral of 1/x^2+a = 1/sqrt(a) .arctan(x/sqrt(a)) + c but not why that was the case, thanks for the video!
@Necrozene3 ай бұрын
I love your stuff man! Love maths. Maths is my "God Zero"!
@wasagamer00110 ай бұрын
Thanks for the video sir !
@stinkybohoon714 ай бұрын
Excellent Teacher, congrats
@TopRankX10 ай бұрын
Keep going man! Love what you do ❤
@jesusandrade13786 ай бұрын
Some integrals require more than 2 or 3 consecutive substitutions or methods to get a solution, and there may be equivalent solutions.
@madsniper59278 ай бұрын
And that was perfect Thank you for the lesson
@michalkorczyk41894 ай бұрын
if this video is too long or slow for you, press F12 and type "document.querySelector(".video-stream").playbackRate = 3;" to konsol
@amolgameryt71599 ай бұрын
I had solved this question recently it kinda esy If you are preparing for competitive examinations
@kawenjanathan65383 ай бұрын
Thank you for the save ❤
@user-kg7xw5ip2l3 ай бұрын
You are my favorite ❤❤❤❤ bro
@jesusmartinez966210 ай бұрын
your videos are the best!
@herbertsusmann9863 ай бұрын
This is why they came out with books of tables of integrals! People doing real work want to look it up in a book and not try to derive it from first principles and probably get a sign wrong or something!
@lukaskamin7557 ай бұрын
Wow, that was intense, kinda a detective story to find the suspect (the integral) LOL
@ethanbartiromo28884 ай бұрын
I actually watch all of your videos in 2x speed lol
@moorecable5 ай бұрын
Learned a lot. But why not let u be cos(X) . Then it's sqrt-(lncos(x)) . You can get ride of the negative as cos(-x) is also cos(x).
@PrimeNewtons5 ай бұрын
If I knew it was a better option, I would have used it.
@user-mj6rr1xn3t10 ай бұрын
Thanks, integral sqrt sen x
@martys99728 ай бұрын
Great derivation, but when tanh instantly turns into tan for v/sqrt(2), at 23:48, you really should have mentioned that correction or edited over it.
@PrimeNewtons8 ай бұрын
I'll have to watch it again to see what you're referring to. Thanks for the feedback.
@bibliophilesayan32010 ай бұрын
Sir can't we use The method of by parts to solve this problem??
@devonwilson57766 ай бұрын
Greetings. Thanks for sharing.
@lebesguegilmar18 ай бұрын
The maestro. Very inteligent your tecnic of solution. The same strategy of solution if the int \sqrt{\cot x}dx? And too \int \sqrt{\sec x}dx? The variable \phy and \theta not same? Here in the Brazil congratulation teacher
@haithamsuneer21827 ай бұрын
Hey sir i hope ur doing well can i ask a doubt after we get the integral as ∫2dt/(t²+1/t²) cant we factor the deno as {(a²+b²) = (a+b)² -(2ab)} SO WE GET 2∫dt/(t+ 1/t)² - √ 2² then just apply the formula so the final answer in terms of t will be 1/√2 {ln [(t+ 1/t)+ √2] / [(t+ 1/t) - √2]} + c
@tamilchelvanramasamy87336 ай бұрын
Great Sir
@piyushhh.5410 ай бұрын
Actually this is a very famous question in our board(exam conducts) education system
@abhishekpathak497310 ай бұрын
That was wonderful ❤
@AvrajitGRoy10 ай бұрын
Amazing man!
@vadimtokman1236 ай бұрын
Could you differentiate to prove there is no errors? BTW, great job!!!!
@PrimeNewtons6 ай бұрын
I did
@noid357110 ай бұрын
I had this setup on my exam and I was stuck, I just couldn't figure out what to do and wasted so much time. So after the exam I put this problem into symbolab, since nobody got the answer, and I couldn't beleve the result Thanks for the video : )
@emmanuelseiman272510 ай бұрын
Cool but sqrt(tanx) +1/sqrt(tanx) is always >1 (ex: 1.46 for π/6) so you have to use coth−1 instead of tanh−1. It is always necessary to pay attention to the domain of definition of hyperbolic trigo. functions tanh−1 ∈ (-1;1) and coth−1 ∈ (-∞;-1)∪(1;∞)
@jesusandrade13786 ай бұрын
You are right
@vashu47110 ай бұрын
I solved this question yesterday in my school in one try ✌️
@Occ8816 ай бұрын
Do you study in college or highschool...you might be genius
@Harbingersknight2110 ай бұрын
Thanks this problem was in my text book
@Vikram-xc3pb6 ай бұрын
Just another ordinary problem for Jee advance aspirants😂😂
@roddos6 ай бұрын
Piękny wywód.
@lindsaywaterman20106 ай бұрын
Brilliant!
@nibirhasan414210 ай бұрын
how can we write root 2 φ as the result of that integration? as tanh^2 x+ sech^2x=1
@paulmatthewduffy10 ай бұрын
WOW!
@Shashi_22710 ай бұрын
Your 📸 are most recommended
@omaraladib21658 ай бұрын
حلوة ولكن الطريقة طويلة
@gideonkudgorgi2267 ай бұрын
O Bruv, why is the answer more complicated than the question itself 😅😅😅😅
@jesusandrade13786 ай бұрын
Because the integral is more complicated than the derivative (the integrand). That is why integration is more difficult than differentiation. Differentiation is just mechanical/algebraic manipulation and simplification, and integration is an art. And many elementary expressions, functions, or integrands don't have elementary integrals/antiderivatives
@user-nd7th3hy4l8 ай бұрын
((tanx)^2)/ 2(tanx)^0,5
@user-nd7th3hy4l6 ай бұрын
-ln(sinX)^0,5
@ache640710 ай бұрын
What do you do for a living? Are you a teacher? You’d make a good one