integral of sqrt of tanx

  Рет қаралды 37,479

Prime Newtons

Prime Newtons

Күн бұрын

Пікірлер: 94
@Moj94
@Moj94 Жыл бұрын
This is one of those integrals that looks "simple enough" when you're taking an exam.
@NWSCS
@NWSCS 2 ай бұрын
This is one of those integrals that just gets way out into the weeds. Multiple substitutions, hyperbolic trig functions. Very challenging. Great job explaining the steps. Especially the ones where someone can easily get lost on.
@paulstjean8598
@paulstjean8598 5 ай 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.
@josephparrish7625
@josephparrish7625 Жыл 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-zr5jo
@savitrinamdeo-zr5jo Жыл бұрын
Very nice way of explanation nice n clear voice
@bravo2992
@bravo2992 Жыл бұрын
I think our plan was to get rid of root
@Gaurav_C_Kher
@Gaurav_C_Kher Жыл 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
@ThembaNzama-q7c
@ThembaNzama-q7c Жыл бұрын
That's great !!!
@sivasakthisaravanan4850
@sivasakthisaravanan4850 9 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😊
@jayniesgottagun
@jayniesgottagun Жыл бұрын
My God, you're smart and have a gift for teaching. I plan to absorb all you have to give.
@jesusandrade1378
@jesusandrade1378 10 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)
@rhm5158
@rhm5158 11 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.
@Jop_pop
@Jop_pop Жыл бұрын
I've never dived this deep into integrals before and this is probably the most complicated integral ive seen explained so succinctly
@syed3344
@syed3344 11 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
@a.anithapreethysiva1542
@a.anithapreethysiva1542 3 ай бұрын
​@@syed3344damn
@paulinofm
@paulinofm 10 ай бұрын
Maravillosa integral y maravillosa solución. Thanks from Spain. !!!!!
@cesarmiranda2205
@cesarmiranda2205 Жыл бұрын
Outstanding explanation, you are the guy, I really enjoyed, best regards from Brazil.
@Hiram_-tg5wr
@Hiram_-tg5wr Ай бұрын
great solution and also a fan of the handwriting. But can we get answer in the form of natural log instead of inverse hyperbolic tangent. We could use the natural log substitution in form of 1/(x^2-a^2).
@murdock5537
@murdock5537 11 ай бұрын
This is amazing. Many thanks for this awesome "journey".
@PrimeNewtons
@PrimeNewtons 11 ай бұрын
Glad you enjoyed it!
@trivikram4962
@trivikram4962 4 ай бұрын
i can finally binge ur videos, as i have just started integration. thanks
@saarike
@saarike 8 ай бұрын
Huh, what an integral. Thanks for sharing. Never stop learning or you not living 👍👌👍I have to watch this many times...
@Viewpoint314
@Viewpoint314 10 ай бұрын
Nice clear writing for this interesting integral.
@NamregSelaur-up4or
@NamregSelaur-up4or 11 ай бұрын
I solved that integral with two maths skills. 1. Using substitucion. 2. Completing the perfect trinomial.
@FedericoNassetti
@FedericoNassetti 6 ай бұрын
Keep going your videos are the highlight of my day❤
@AshokKumar-ul6dg
@AshokKumar-ul6dg 3 ай бұрын
Thanks - you always make it so simple and intuitive. ...A hallmark of a genius-teacher. 🎉❤ A small observation. The first term has + sign and the second term has -. ( I is inv tan exp and the second is hyp as derived. In the last step, by oversight you have inverted u and v. ( Happens to me always over the board😢)...
@arungosavi5698
@arungosavi5698 11 ай бұрын
Mind boggling ,sir
@bittuKumar-sw3ux
@bittuKumar-sw3ux 2 ай бұрын
From India absolutely amazing sir
@michalkorczyk4189
@michalkorczyk4189 8 ай бұрын
if this video is too long or slow for you, press F12 and type "document.querySelector(".video-stream").playbackRate = 3;" to konsol
@VishwanathMN-m5i
@VishwanathMN-m5i Жыл бұрын
Sir you are a genius at mathematics thank you
@haithamsuneer2182
@haithamsuneer2182 11 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
@omxky
@omxky 3 ай бұрын
Love your dedication BRO keep samshin integrals
@maxborn7400
@maxborn7400 Жыл 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).
@lukaskamin755
@lukaskamin755 11 ай бұрын
Wow, that was intense, kinda a detective story to find the suspect (the integral) LOL
@stinkybohoon71
@stinkybohoon71 8 ай бұрын
Excellent Teacher, congrats
@rob876
@rob876 Жыл бұрын
You made a difficult integral look easy.
@TopRankX
@TopRankX Жыл бұрын
Keep going man! Love what you do ❤
@عابرون-ن7ذ
@عابرون-ن7ذ Жыл бұрын
Good math go head for more thank you man 👍👍👍
@bibliophilesayan320
@bibliophilesayan320 Жыл бұрын
Sir can't we use The method of by parts to solve this problem??
@nitishjha8259
@nitishjha8259 3 ай бұрын
Different level of problem. Very nice..
@oscarfranciscosantanafranc8948
@oscarfranciscosantanafranc8948 10 ай бұрын
You are very smart. God bless you!
@servictorovich2576
@servictorovich2576 Жыл бұрын
однозначно, красивое решение. Достойно похвалы
@jesusandrade1378
@jesusandrade1378 10 ай бұрын
Some integrals require more than 2 or 3 consecutive substitutions or methods to get a solution, and there may be equivalent solutions.
@ethanbartiromo2888
@ethanbartiromo2888 9 ай бұрын
I actually watch all of your videos in 2x speed lol
@martys9972
@martys9972 Жыл 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.
@PrimeNewtons
@PrimeNewtons Жыл бұрын
I'll have to watch it again to see what you're referring to. Thanks for the feedback.
@joelmacinnes2391
@joelmacinnes2391 9 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!
@jesusmartinez9662
@jesusmartinez9662 Жыл бұрын
your videos are the best!
@nibirhasan4142
@nibirhasan4142 Жыл бұрын
how can we write root 2 φ as the result of that integration? as tanh^2 x+ sech^2x=1
@madsniper5927
@madsniper5927 Жыл бұрын
And that was perfect Thank you for the lesson
@Necrozene
@Necrozene 7 ай бұрын
I love your stuff man! Love maths. Maths is my "God Zero"!
@wasagamer001
@wasagamer001 Жыл бұрын
Thanks for the video sir !
@WazifatutTiyebah
@WazifatutTiyebah 3 ай бұрын
Thank you soooooo much! I was helped a lot by this!
@AngelZangata
@AngelZangata 8 ай бұрын
You are my favorite ❤❤❤❤ bro
@moorecable
@moorecable 9 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).
@PrimeNewtons
@PrimeNewtons 9 ай бұрын
If I knew it was a better option, I would have used it.
@lebesguegilmar1
@lebesguegilmar1 Жыл 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
@tamilchelvanramasamy8733
@tamilchelvanramasamy8733 11 ай бұрын
Great Sir
@amolgameryt7159
@amolgameryt7159 Жыл бұрын
I had solved this question recently it kinda esy If you are preparing for competitive examinations
@noid3571
@noid3571 Жыл 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 : )
@kawenjanathan6538
@kawenjanathan6538 7 ай бұрын
Thank you for the save ❤
@roddos
@roddos 10 ай бұрын
Piękny wywód.
@vadimtokman123
@vadimtokman123 11 ай бұрын
Could you differentiate to prove there is no errors? BTW, great job!!!!
@PrimeNewtons
@PrimeNewtons 11 ай бұрын
I did
@devonwilson5776
@devonwilson5776 11 ай бұрын
Greetings. Thanks for sharing.
@AvrajitGRoy
@AvrajitGRoy Жыл бұрын
Amazing man!
@vashu471
@vashu471 Жыл бұрын
I solved this question yesterday in my school in one try ✌️
@Occ881
@Occ881 10 ай бұрын
Do you study in college or highschool...you might be genius
@abhishekpathak4973
@abhishekpathak4973 Жыл бұрын
That was wonderful ❤
@Harbingersknight21
@Harbingersknight21 Жыл бұрын
Thanks this problem was in my text book
@herbertsusmann986
@herbertsusmann986 8 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!
@ChalkyWhiteChalkyWhite
@ChalkyWhiteChalkyWhite 3 ай бұрын
Facts
@emmanuelseiman2725
@emmanuelseiman2725 Жыл 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;∞)
@jesusandrade1378
@jesusandrade1378 10 ай бұрын
You are right
@piyushhh.54
@piyushhh.54 Жыл бұрын
Actually this is a very famous question in our board(exam conducts) education system
@JotaMartinez-c1q
@JotaMartinez-c1q Жыл бұрын
Thanks, integral sqrt sen x
@lindsaywaterman2010
@lindsaywaterman2010 10 ай бұрын
Brilliant!
@Shashi_227
@Shashi_227 Жыл бұрын
Your 📸 are most recommended
@paulmatthewduffy
@paulmatthewduffy Жыл бұрын
WOW!
@martyknight
@martyknight 4 ай бұрын
Wow
@omaraladib2165
@omaraladib2165 Жыл бұрын
حلوة ولكن الطريقة طويلة
@gideonkudgorgi226
@gideonkudgorgi226 11 ай бұрын
O Bruv, why is the answer more complicated than the question itself 😅😅😅😅
@jesusandrade1378
@jesusandrade1378 10 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
@Bertin-q3y
@Bertin-q3y Жыл бұрын
((tanx)^2)/ 2(tanx)^0,5
@antoniopena1183
@antoniopena1183 3 ай бұрын
Damn
@Bertin-q3y
@Bertin-q3y 10 ай бұрын
-ln(sinX)^0,5
@Vikram-xc3pb
@Vikram-xc3pb 11 ай бұрын
Just another ordinary problem for Jee advance aspirants😂😂
@ache6407
@ache6407 Жыл бұрын
What do you do for a living? Are you a teacher? You’d make a good one
@maximusmeridius2060
@maximusmeridius2060 6 күн бұрын
I can do this with my eyes closed now
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