Integral of sin^4(x)
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- Опубліковано 20 вер 2024
- Integral of sin^4(x) , integral of sin^4x
solution playlist page www.blackpenred...
trig integrals, trigonometric integrals, integral of sin(x), integral of tan(x), integral of sec(x), James Stewart single variable Calculus sect 7.2, integration examples, integral examples, antiderivative examples, u substitution examples, integral practice problems, calculus 2 practice problems, blackpenredpen,
The best thing about your videos is that you dont skip any steps while explaining. You write every trivial step on the board.
keep up the good work. All the best
S
Not only is he good at math, he also has a thermal detonator.
Thermal detonator is only like Mike 🎤but it's shape is only Round
I can't understand why this comment has 237 likes
Lol😆😆
@@MigueelHoO Are you from which country??
@@no_onecares3266 bc a lot of people like me were wondering what that round tech thing is.
@@Zahra27756 🖕🖕🖕🖕🖕
If only university professors would explain things half this well.
it's pretty common that they are good at experiment and researching but not teaching cause that's not what professors want to concentrate on and they don't take education courses and credits.
Do they this in Universities really? It's taught in High School in India, perhaps it's a easier question for most indian science student
@@foreverknight3448 Good For You
This is highschool subject tho...
@@foreverknight3448 same
I need such kind of teacher
RESPECT FROM INDIA🇮🇳
had this on test review, and was stuck! So happy you did this one. Best math youtube channel!!!
Page 76, Integral 14.350 in Spiegel's Mathematical Handbook. Just as you say. Have you read that sometime in his childhood, Feynman spent most of a summer holiday working out all the integrals in a handbook...without cheating by looking at the solutions first?
Who would ever have thought that a dumb retired old bloke would get such pleasure from watching and learning integral solving. Thank you.... live long and prosper;-)
"Let no corrupt communication proceed out of your mouth, but that which is good to the use of edifying, that it may minister grace unto the hearers." (Blue Letter Bible, KJV, Ephesians 4:29)
We can also get reduction formula from integration by parts and pythagorean identity
you explain very fucking well and I love your accent, thank you
Dawich Dawichis thank you f*cking much too!
I was trying to integrate this to find the hyper volume of a 5d sphere embedded in spherical space, and I was struggling hard. The surface of a 5D sphere embedded in spherical space can be measured with ((8)(pi^2)((sin(r))^4)/3)
Bro your explanation is soo gooddd😭😭😭 every step explained in detailllll 😭😭😭 thanksss bro 😭😭✨✨✨
Why can't my textbook explain it like this :/ Thanks :)
You're welcome
Well, in india textbooks can also explain it..😂 usually we use old books thus our seniors have already written a hint of that question or sometimes whole solution :)
Thank you, I benefited a lot from you. Greetings of love and respect to you from Iraq 🇮🇶 🧡
Hey, It would be easier if we use reduction formula....
Naveen Madhan I have never learned that lol
@@PKPS01238 you can go and check professor Leonard he has a vid explaining it
@@PKPS01238 reduction is way easy, you'll pick up fast.
You’re a great tracher. Thank you for posting such instructive videos.
you can use this
1=(sin²(x)+cos²(x
(cos(2x)=sin²(x) - cos²(x
and you can somme two equation for reveled more
Nope cos(2x)=cos^2(x) - sin^2(x).
02:28 What happened to the binomial formula? It would be shorter to calculate this way...
But it would be even better to temporarily "hide" the ugly cosines under some 1-letter symbols during simplifying, and back-substitute the cos(2x) later.
but if you differentiate the answer you get 1/8cos(4x)-1/2cos(2x)+3/8, how is that (sin(x))^4 ?
Awesome video you explain every step flawlessly.
I'm from Iraq and your videos are so helpful thank you sooooooooooooooooo much
The intergral For Fonction Sin Et Cos Et Tan its Dificule
gracias por la explicación, saludos desde Perú
Still helpful after so long Year🎉
Thank you from Bangladesh LOVE
++++HELPED A LOT ++++++
SAFIN AHMED
Nicely explained, thank you! However, you forgot some parentheses on the right side of the whiteboard. Doesn't really matter, it's clear anyway.
I wish university professors explain like that. You explained with great details without skip any process. Thank you !!! :-)
Renan seriously 🙄!!!
Bcz in india 12th std. Student can solve this in very easily
You are University student yet you need explanation ??
Disgusting
@@no_onecares3266 Yeah I should go to India and study math there.
@@renan6827 "Atidhi devo bhavah" Most welcome 🙂
Sister/ brother I teach you definitely
@@renan6827 are you girl/boy??
@@no_onecares3266 I am a man!!!
So helpful, thank you so much for making these videos
omg thank you :D I couldn't get why theres 3x/8 fraction...just now after three hours it hit me thanks to your explanation... omg I'm so dumb lol thanks
I've just finished the same problem using integration by parts:
-sin^3(x)dcos(x)
Wow sir you're awesome..
The best explanation ever ! Thanks a lot bro 💖
Yayyyy ! I had fun calculating along with you. Thanks for helping !
What class you are taught this in your country. In my case Nepal it's taught in class 11
bro ur the best maths teacher. keep making more videos
Love from india THANK FOR MAKING SUCH TYPE VIDEO THAT HELP US A LOT
Really good explanation love it
WAIT, at 3:57 when you're multiplying, shouldn't it be cos(2x)/2 rather than cos(4x)/2? I can't understand the reasoning behind this. Help me please!
Jake Goykia Power reduction, its cos(2*2x) 4x is correct
using sin^3x.sinx , my answer comes out 4times of what you have.
Can we express sin^4(x) as a sum of sin and cos using the complex exponential formulae and then integrate from there?
Was struggling with this one, you saved me, that's why I love Asians😞💞💞💞
melhores aulas sempre. valeu !!!
You should’ve told them about the rule of (a-b)^2=a^2 -2ab+b^2 😇
Very nicely presented! 😊 Thanks! The GHOSTS OF DEPARTED QUANTITIES SALUTE YOU! 😊
The "Ghosts of Departed Quantities" refers to the furious debates regarding infinitesimals in Newton's time and later. It was intended critically, but I think it is a splendid metaphor for differential quantities. And it is said: THE DERIVATIVE DISINTEGRATES THE INTEGRAL! 🌻✨🌟🌻🌈🌎🌝
Very nicely presented! 😊 Thanks! The GHOSTS OF DEPARTED QUANTITIES SALUTE YOU! 😊
The "Ghosts of Departed Quantities" refers to the furious debates regarding infinitesimals in Newton's time and later. It was intended critically, but I think it is a splendid metaphor for differential quantities. And it is said: THE DERIVATIVE DISINTEGRATES THE INTEGRAL! 🌻✨🌟🌻🌈🌎🌝
ở bên nước ngoài có học công thức hạ bậc k nhỉ, anh này giảng dễ hiểu quá
does the same principle apply if ur doing sin^4 (3x) dx ?
Yes. Just make sure that when you do the Power Reduction Formula for the first time, that you have cos(6x) instead of cos(2x). When reducing the power, the argument of the trig function doubles.
`int(sin4x)/(sin^(4)x)dx`
What is the solution of this question
You're a great teacher!
Why does it not become negative ((sinx)^5)/(5cosx) ?
Is this the same as hyperbolic function? If i want to integrate sinh⁴(x) and follow this video, the answer is same?
Do you refer Indian textbooks for questions? Cause I do see some similarities
where does the 1/2 come from infront of 1-cos(x) and why do you have it there for the integral of sin^4 and not there when you integrate sin^3 and sin^5
Multiplying by 1/2 is like dividing by two so instead of writing the formula (1-cos^2(x))/2 he writes 1/2 · cos^2(x)
Your explanation is amazing👏
That's really helps me
Thanks
محد عرف يفهمني غيرك ❤
I dont understand how u got the 1/2+1/2cos (4x)...please explain
يو آني موسيسي تاريب using half angle formula.
nice job yo I am doing mat233 worksheet this really helpful
sound problem....it's very low
thanks man, your videos really helpful.
Bro i got the same answer but my teacher showed me another answer so im confused? The answer was (3x/2 -1/4sin(2x) +1/4sin(4x)+c
This question sounds easy. But its actually not. You teach so good. Now I am master in it. LOL🤔🤔🤗🤗
Since i have plans to finish my studies, you review me of integral calculus
yay!
It is still helpful in 2021
Thx sir but can u keep it cam in front of it
I did it with your DI method easily by taking sin^x in d side and sinx in i side 😘
Hey hero...
Keep going
You are good at teaching
Can you pleeease make a video explaining something like integral of sin^4(x)cos^2(x) ?
Plz take limit "0" to "t" and Solve it through convolution theorem
that was great bro.. thankfull for the answer, it's helpfull. :) keep moving forward :)
Thanks!
Can u explain why we need to use power reduction rule @0:40
Thank You! This was really helpful!
I am from india and i loved ur method to solve this
wew u explain good thanks man
Thank you , brother 🔥❤️
So the power reduction formula is the same for sin and cos? That doesn't seem right
They are different. For sine is - but for cosine is +
blackpenredpen Missed that! Makes sense when you think of sin^2(x)+cos^2(x)=1
Where does the power reduction formula come from?
+Joaquin Pirotto double angle formula for cos(2x)=cos^2x -sin^2x
Thank you! You saved me wiht my homework
its crazy how math hasnt changed in 5 years
thank you! I've been trying this on the online integral calculator but I don't get it. I get it now, thanks to you.
Is that ur real photo in the dp?
@@vasunith9682 google Yoo Jeongyeon.
@@theroadnottaken_ okay
Blackpen redpen is korean?
@@vasunith9682 I'm not her, but you should definitely check her out. To answer your question, she is indeed korean. Go watch Jeongyeon fancams on youtube! :)
dx/(sinx)^4 ??? ...
tan^3x/3 +tanx
Great job
Where did you get that identity? O.o
Please explain loudly
Thank you so much!
You’re a legend 🙏🏾
3:26 did he just explained that in his native language
i need integral 1/1+x^5 and x^x and 1/1-x^7
Use for the 1st and 3rd integral partial fraction decomposition and for the 2nd integral the power of e^ln(x^x).
Integration of sinx is -cosx
- (cosx sinx^3)/4 + 3/4 [- cosx sinx/2 +1/2 x] +c is better
Why dont we use sin²x = 1-cos²x ??
Found youu
try get terms in linear power it is esay to solve
What is the Integral of Sin(pi/4) ?
Please answer I need this urgently. Thank you.
Sin(pi/4) is a constant, it equals (√2)/2. The integral of (√2)/2 is (√2x)/2
my math teacher did it with eulers formula 😢
Thanks from Algeria
I never thought the answer is solved in like this 😂
what is integration of (π-x)^2??????
depends on what you're integrating it with respect to
With respect to x, it's ((π-x)^3)/-3
integral of (ax + b)^n = (ax + b)^(n+1) / ( a*(n+1) )
Because a (-1) and b (π) are both constant, you can use this formula.
It only works for linear transformations of x.
I belongs to India very good sir
شكرا لك من العراق
Sin este chino no paso el semestre
Thank you so much sir
you know the power reduction formula (not so useful) and you don't know the this: (a+b)^2 = a^2 + 2ab + b^2 ??
xristos bart He didn't work with (a+b)^2. He worked with (a-b)^2. And he did it correctly.
Thank you thank you!
Genius literally
Legend understood whole numerical at 1:23
I am indian + smart
That's why I understood this whole numerical within first 3 steps.
Same 😁
@@lakshitajoshi8847 👏😌