Integrating using t=tan(x/2) substitution - [The Weierstrass substitution]
In this video, I showed how to integrate a function of the form 1/(c + bsinx +acosx) .
Жүктеу.....
Пікірлер: 62
@jan-willemreens9010 Жыл бұрын
... Newton, what I forgot to say is, keep doing your presentations on the blackboard with just a simple piece of chalk, your handwriting is excellent for this! Jan-W
@PrimeNewtons
Жыл бұрын
Thanks for your feedback. It means a lot.
@jcmarketingblog375
Жыл бұрын
This channel has really come at the right time, thank you Newton🙏🙏
@electricitysexenergy1509
11 ай бұрын
Which level
@kinyerajoel97319 күн бұрын
I am a teacher, but whenever I watch your video, everything is just fine to teach
@boydbanda1912 Жыл бұрын
Big man you're doing it more than anyone. I like the way you Tutor us. Keep up the good work manh.
@PrimeNewtons
Жыл бұрын
Thank you. Your comment sounds African 😀. Where are you from?
@robread-jones3698 Жыл бұрын
Thanks Newton, that was so good. I really enjoyed that. Keep up the great videos. 👍
@Ni999
Жыл бұрын
Same here. 👍
@romanmuller99725 күн бұрын
Wow, this is a great video. You have such an excitement inducing voice. You're really getting the beauty of maths across.
@dusscode9 ай бұрын
You can actually solve it much more simply by multiplying the numerator and denominator by the conjugate of the denominator, to get ∫ (1-sin(x))/cos^2(x) dx.
@Koolasuchus8
6 ай бұрын
Yeah but this method is very very useful for integrals that are impossible to figure out using other methods without already knowing the answer and working back. Its hard to explain but the "t method" is a very useful tool that some rusty person could use to solve integrals he is unprepared for or cant see the shortcut. Put simply its inductive not deductive. This is an easy example of the t rule.
@willwill39172 ай бұрын
you are a perfect teacher, moreover a perfect human
@paulmatthewduffy6 ай бұрын
Excellent refresher. Thank you.
@_vblax3 ай бұрын
life saver! great explanation, thank you!
@halimsemihozcan8526Ай бұрын
Thanks for this lesson . You are a good teacher .
@mb-hv6kfАй бұрын
Thank you for the nice example and exposition. Added another tool to the toolkit.
@user-ej1sk7zm3j5 ай бұрын
Newton.. sincerely speaking you have helped me alot..🙏
@PrimeNewtons
5 ай бұрын
Glad to hear that
@user-ej1sk7zm3j
5 ай бұрын
@@PrimeNewtons thank u..I'm a Kenyan student
@ndzalamankwinika29999 ай бұрын
You are a good teacher, sir
@stevemwanza7521 Жыл бұрын
Clearly explained 👏👏 Thanks
@senayurekyakan22484 ай бұрын
best teacher ever
@levisim997 Жыл бұрын
Very helpful! ❤
@sssoupАй бұрын
Excellent !
@arungosavi56986 ай бұрын
Brilliant way to solve sir
@ThenSaidHeUntoThem Жыл бұрын
Thank you! 😊
@georgesadler78309 ай бұрын
Professor Prime Newtons, thank you for the video. Calculus Two playlist on KZread does not cover this topic. This topic is called special substitution, which is part of Techniques of Integration in Calculus Two. This is an error free video/lecture on KZread TV with Professor Prime Newtons.
@lunaresting Жыл бұрын
Thanks a lot man
@fortunateonka9 ай бұрын
Well explained sir❤
@erms_2342 ай бұрын
amazing
@chappel99986 ай бұрын
Amazing video. You are so damn smart.
@Bulbo_2156 ай бұрын
Loved it
@utuberaj6011 ай бұрын
Nice way to get the answer. But Mr Newton, I did it WITHOUT any substitution. In fact all I did was multiply and divide by the conjugate of the DENOMINATOR ( 1 - Sin X) and there onwards ,it is quite simple really for a good Calc 1 or Calc 2 level student. Your method, though a nice U-sub, seems quite lengthy, if I may say, Mr Newton. To make this a little harder, why not try to solve the same Integral as a DEFINITE integral from 0 to pi/2? It is quite an interesting one indeed, trust me❤❤
@PrimeNewtons
11 ай бұрын
I'll give it a shot soon
@mehakghous7884
8 ай бұрын
Well for your information "SIR", this method (sir newton's one) really saved me since i had to do the integration USING this method in my calculus paper. Although your method is right, i guess your knowledge has made you arrogant, and you are trying hard to prove your supremacy to everyone by spreading hatred on the internet, and i guess that's why you're not teaching here with thousands of subscribers. have a great day "❤❤❤❤"
@adebayoisraeladeshola10 күн бұрын
Thanks sir
@jan-willemreens9010 Жыл бұрын
... A good day to you Newton, Right out of one of my " old and trusted " little math notebooks regarding integrals the following solution path in short: Given INT(1/(1 + sin(x))dx [ multiply top and bottom of the integrand by (1 - sin(x)) ] --> INT((1 - sin(x))/(1 - sin^2(x)))dx = INT((1 - sin(x))/cos^2(x))dx = INT(1/cos^2(x))dx + INT(- sin(x)/cos^2(x))dx [ u = cos(x) --> du = - sin(x)dx ] = INT(sec^2(x))dx + INT(1/u^2)du = tan(x) + INT(u^-2)du [ applying the good old REVERSE power rule, remember Newton? (lol) ] = tan(x) - 1/u [ u = cos(x) ] = tan(x) - 1/cos(x) + C = tan(x) - sec(x) + C = (sin(x) - 1)/cos(x) + C ... etc etc ... I leave the outcome to everyone's preference ... Thank you too Newton for your great performance; I really mean this, an eye opener for me; isn't it called the Weierstrass method? A pleasant weekend to you, Jan-W
@PrimeNewtons
Жыл бұрын
Yes! This is an alternative. I call it 'rationalization'. I just get scared with the integral of secx or sec²x or sec³x. They scare me. But certainly, in recent times I have used that until I found my old Engineering Math book by K. A. Stroud. Then it all came back to me. We are dealing with the cold and rains here. It's never been like this before. Now I appreciate sunshine 🌞. And thank you for helping with the name. Truly it's called the Weierstrass Substitution
@RaadoNoori-km5ejАй бұрын
That is great, but I have question could we use t= tanx Or we have to make angle x/2
@EE-Spectrum3 ай бұрын
Is there a relationship between t-substitution and the half-angle identities?
@joseantonioandrade2808Ай бұрын
Newton you can also solve that integral using the conjugate of 1+sinx , that is multiplying up and the bottom by 1- sinx, and the final result is tanx-secx, just another way to do it. greetings
@jusajiggynigga2524 Жыл бұрын
love your content bro
@mikedavis76368 ай бұрын
I multiplied the numerator and denominator by the conjugate, 1 - sin X, got 1 - sin x/1-sin²X, substituted Cos²X for 1-sin²X, split the fraction, took the integral and ended up with tan x - sec X + c
@theandrewadler
7 ай бұрын
That's really smart. Good job
@hazwi
6 ай бұрын
i did the exact same process
@deborahatobrah68273 ай бұрын
I like u boss
@estevaocachiliva3249Ай бұрын
Great video professor👏🏽 I have two questions: 1 - can I use this t substituion whenever I have a integral of cosine and sine? And if I have another trigonometric identity can I rewrite this identity in terms of sine or cossine or both to apply this substituion? 2 - how can I apply this substituion in those cases I have in the answer a angle in radians summing the variable on the argument of some trigonometric identity. Like for exemplo how to apply t substituion on the integral of dx/ sen(x) + cos(x). The answer of this integral is 1/sqrt 2 that multiply ln( csc( x + pi/4) - cot( x + pi/ 4) How can I reach the same result with t substituion.
@mattiollikainen8098
Ай бұрын
Very good.
@split98533 ай бұрын
How come the day after ive had my calculus 2 exam this video gets recomended 😒
@adebayoisraeladeshola10 күн бұрын
What if there are non linear function
@swarnabhamitra72336 ай бұрын
Just use sinx=(2tan(x/2)) /(1+tan^2(x/2) ) =(2tan(x/2)) /(sec^2(x/2)) it becomes simple by half and double angles relations
@VENOMx007x9 ай бұрын
Sir you also do it by substituting sinx with 2tanx/2 upon 1+tan square x/2
@domanicmarcus21766 ай бұрын
Why did you choose x over 2 and not just Theta?
@PrimeNewtons
6 ай бұрын
That's the substitution that works
@kurtecaranum30472 ай бұрын
If you remember all your derivatives, the integral could be solved as (1 - sin x)/(cos^2 x) dx (sec^2 x - sec x tan x) dx tan x - sec x + C
@d.yousefsobh70107 ай бұрын
Sir you also do it by substituting 1+sinx=
@TSR19426 ай бұрын
Try by multiplying the denominator and numerator with conugate.
@domanicmarcus21768 ай бұрын
Can we go backward? We now that sin^2(x)+cos^2(x) =1. Can we sub sin^2(x)+cos^2(x) for 1 and then separate our fractions like this: sin^2(x)/(1+sin(x)) +cos^2(x)/(1+sin(x)) and then keep manipulating our algebra to solve the problem in the video? Please let me know if it is possible? Thank You
@chuckc36654 ай бұрын
this is a very bad method, you should trig identities
Пікірлер: 62
... Newton, what I forgot to say is, keep doing your presentations on the blackboard with just a simple piece of chalk, your handwriting is excellent for this! Jan-W
@PrimeNewtons
Жыл бұрын
Thanks for your feedback. It means a lot.
@jcmarketingblog375
Жыл бұрын
This channel has really come at the right time, thank you Newton🙏🙏
@electricitysexenergy1509
11 ай бұрын
Which level
I am a teacher, but whenever I watch your video, everything is just fine to teach
Big man you're doing it more than anyone. I like the way you Tutor us. Keep up the good work manh.
@PrimeNewtons
Жыл бұрын
Thank you. Your comment sounds African 😀. Where are you from?
Thanks Newton, that was so good. I really enjoyed that. Keep up the great videos. 👍
@Ni999
Жыл бұрын
Same here. 👍
Wow, this is a great video. You have such an excitement inducing voice. You're really getting the beauty of maths across.
You can actually solve it much more simply by multiplying the numerator and denominator by the conjugate of the denominator, to get ∫ (1-sin(x))/cos^2(x) dx.
@Koolasuchus8
6 ай бұрын
Yeah but this method is very very useful for integrals that are impossible to figure out using other methods without already knowing the answer and working back. Its hard to explain but the "t method" is a very useful tool that some rusty person could use to solve integrals he is unprepared for or cant see the shortcut. Put simply its inductive not deductive. This is an easy example of the t rule.
you are a perfect teacher, moreover a perfect human
Excellent refresher. Thank you.
life saver! great explanation, thank you!
Thanks for this lesson . You are a good teacher .
Thank you for the nice example and exposition. Added another tool to the toolkit.
Newton.. sincerely speaking you have helped me alot..🙏
@PrimeNewtons
5 ай бұрын
Glad to hear that
@user-ej1sk7zm3j
5 ай бұрын
@@PrimeNewtons thank u..I'm a Kenyan student
You are a good teacher, sir
Clearly explained 👏👏 Thanks
best teacher ever
Very helpful! ❤
Excellent !
Brilliant way to solve sir
Thank you! 😊
Professor Prime Newtons, thank you for the video. Calculus Two playlist on KZread does not cover this topic. This topic is called special substitution, which is part of Techniques of Integration in Calculus Two. This is an error free video/lecture on KZread TV with Professor Prime Newtons.
Thanks a lot man
Well explained sir❤
amazing
Amazing video. You are so damn smart.
Loved it
Nice way to get the answer. But Mr Newton, I did it WITHOUT any substitution. In fact all I did was multiply and divide by the conjugate of the DENOMINATOR ( 1 - Sin X) and there onwards ,it is quite simple really for a good Calc 1 or Calc 2 level student. Your method, though a nice U-sub, seems quite lengthy, if I may say, Mr Newton. To make this a little harder, why not try to solve the same Integral as a DEFINITE integral from 0 to pi/2? It is quite an interesting one indeed, trust me❤❤
@PrimeNewtons
11 ай бұрын
I'll give it a shot soon
@mehakghous7884
8 ай бұрын
Well for your information "SIR", this method (sir newton's one) really saved me since i had to do the integration USING this method in my calculus paper. Although your method is right, i guess your knowledge has made you arrogant, and you are trying hard to prove your supremacy to everyone by spreading hatred on the internet, and i guess that's why you're not teaching here with thousands of subscribers. have a great day "❤❤❤❤"
Thanks sir
... A good day to you Newton, Right out of one of my " old and trusted " little math notebooks regarding integrals the following solution path in short: Given INT(1/(1 + sin(x))dx [ multiply top and bottom of the integrand by (1 - sin(x)) ] --> INT((1 - sin(x))/(1 - sin^2(x)))dx = INT((1 - sin(x))/cos^2(x))dx = INT(1/cos^2(x))dx + INT(- sin(x)/cos^2(x))dx [ u = cos(x) --> du = - sin(x)dx ] = INT(sec^2(x))dx + INT(1/u^2)du = tan(x) + INT(u^-2)du [ applying the good old REVERSE power rule, remember Newton? (lol) ] = tan(x) - 1/u [ u = cos(x) ] = tan(x) - 1/cos(x) + C = tan(x) - sec(x) + C = (sin(x) - 1)/cos(x) + C ... etc etc ... I leave the outcome to everyone's preference ... Thank you too Newton for your great performance; I really mean this, an eye opener for me; isn't it called the Weierstrass method? A pleasant weekend to you, Jan-W
@PrimeNewtons
Жыл бұрын
Yes! This is an alternative. I call it 'rationalization'. I just get scared with the integral of secx or sec²x or sec³x. They scare me. But certainly, in recent times I have used that until I found my old Engineering Math book by K. A. Stroud. Then it all came back to me. We are dealing with the cold and rains here. It's never been like this before. Now I appreciate sunshine 🌞. And thank you for helping with the name. Truly it's called the Weierstrass Substitution
That is great, but I have question could we use t= tanx Or we have to make angle x/2
Is there a relationship between t-substitution and the half-angle identities?
Newton you can also solve that integral using the conjugate of 1+sinx , that is multiplying up and the bottom by 1- sinx, and the final result is tanx-secx, just another way to do it. greetings
love your content bro
I multiplied the numerator and denominator by the conjugate, 1 - sin X, got 1 - sin x/1-sin²X, substituted Cos²X for 1-sin²X, split the fraction, took the integral and ended up with tan x - sec X + c
@theandrewadler
7 ай бұрын
That's really smart. Good job
@hazwi
6 ай бұрын
i did the exact same process
I like u boss
Great video professor👏🏽 I have two questions: 1 - can I use this t substituion whenever I have a integral of cosine and sine? And if I have another trigonometric identity can I rewrite this identity in terms of sine or cossine or both to apply this substituion? 2 - how can I apply this substituion in those cases I have in the answer a angle in radians summing the variable on the argument of some trigonometric identity. Like for exemplo how to apply t substituion on the integral of dx/ sen(x) + cos(x). The answer of this integral is 1/sqrt 2 that multiply ln( csc( x + pi/4) - cot( x + pi/ 4) How can I reach the same result with t substituion.
@mattiollikainen8098
Ай бұрын
Very good.
How come the day after ive had my calculus 2 exam this video gets recomended 😒
What if there are non linear function
Just use sinx=(2tan(x/2)) /(1+tan^2(x/2) ) =(2tan(x/2)) /(sec^2(x/2)) it becomes simple by half and double angles relations
Sir you also do it by substituting sinx with 2tanx/2 upon 1+tan square x/2
Why did you choose x over 2 and not just Theta?
@PrimeNewtons
6 ай бұрын
That's the substitution that works
If you remember all your derivatives, the integral could be solved as (1 - sin x)/(cos^2 x) dx (sec^2 x - sec x tan x) dx tan x - sec x + C
Sir you also do it by substituting 1+sinx=
Try by multiplying the denominator and numerator with conugate.
Can we go backward? We now that sin^2(x)+cos^2(x) =1. Can we sub sin^2(x)+cos^2(x) for 1 and then separate our fractions like this: sin^2(x)/(1+sin(x)) +cos^2(x)/(1+sin(x)) and then keep manipulating our algebra to solve the problem in the video? Please let me know if it is possible? Thank You
this is a very bad method, you should trig identities
Which level sir