Application of Integration - Free Formula Sheet: bit.ly/3ZdKSnK Calculus 1 Final Exam Review: ruclips.net/video/WmBzmHru78w/видео.html Next Video: ruclips.net/video/TLw8xbmnY3c/видео.html
I don't know why we gotta pay for tuition and crappy professors when we got this legend. They should honestly just assign these videos and give us the exams because that's basically what college has come to for me lmao. Thanks OCT for everything, you have no idea what you've got me through.
The best part is when you get a job and they look at you funny when you try doing calculus and tell you to stick to your job ordering silicone. Not that I've had that experience or anything. Welcome to the world of proving your worth by suffering through math you don't need.
Bro I literally owe you my math classes, I started watching your vids when I was on 7th grade and now I'm a first year Civil engineering student. I gotta say your videos carried me a lot in my class. I swear when I get a job I'll donate a lot to you
Honestly I want to genuinely thank you so much for uploading your videos. You are very intelligent and a consummate teacher. you are so patient and sympathetic when you teach . Your videos have gotten me through Ap courses in highschool , and I would not be continuing my advanced courses without your lectures. Whenever I do not get something , I come to your videos. Words cannot explain how greatful and lucky I am to be able to view your videos . THANK YOU . I have never commented on any youtube videos before , but this is an expection , because your channel is my life savior . Keep doing what you do , all my classmates know about you , and we just have a study group and surround ourselves with your videos . We were wondering if you could do an Ap exam practice video before May 1st . We have a chemistry Ap exam and a Physics 1 exam on May 2nd . we have already watched your previous videos on a lot of the concepts you have made, and they were beyond helpful . The physics ap exam for us is different this year , I am in grade 11 , and they split the examination into two parts . Physics 1 includes all the grade 11 topics plus momentum , rotational motion , and i forget the last unit that was added , but I will let you. Please let me know if you could do this type of video , because I know a lot of people who would find this useful . Again , thank you so much for everything . I love you so much . If you need a schedule on what we learnt , let me know as well .
Thank you Thank you Thank you! Your videos have saved my Calculus 2 grade's life! It so easy to follow you step by step and some of the algebraic tricks you use are so helpful! Glad I found you on RUclips!
I got below-average score for math when I took entrance exam (400/1000), but because of your video and I constantly watched and took notes from your videos, I got A for Calculus and even chemistry. Watching your videos, the complicated concepts become super easy, Thank you very much ;)
I can't believe I'n just finding out about your channel now. You would have saved me when I was finishing my bachelor's degree in civil eng'g. But right now honestly you're helping me understand the concepts and basically right out solving problems that I literally would not have solved on my own. I'm about to take my licensure exams this coming November 2019 and you are saving my a$$! I can't afford to enrol myself in a review center, but here you are, offering your knowledge for free. Thank you so much and I hope you continue what you do, as you are obviously helping a lot of students not only pass their subjects, but to fully understand them as well. Kudos to you and God bless you!
Professor Organic Chemistry Tutor, thank you for another incredible video/lecture on Finding the Surface Area of Revolution in Calculus. I had problems with this topic in years past, however by doing a ton of problems and watching videos, my understanding of this material has drastically improved. This is an error free video/lecture on RUclips TV with the Organic Chemistry Tutor.
Got exactly what I came looking for. My textbook/professor has us memorizing different formulas for different orientations/rotations on the plane. Its much easier when these 'changes' in the formula were described as a radius of the circular slice. Visualization>memorization
It took me awhile to figure out how that graph stuff works, but after that these equations became easier to solve. Thanks TOCT. If I pass my Calculus 2 this semester. I'm definitely going to show my support by donating. Appreciate it.
Like I don’t understand why school has to make things so hard. Just help us to prepare for the test like this. We don’t need to know about the theories and all that. Just show examples, then explain why its like this. Thank you so much! This is much easier than I thought!
Question starting at 12:38. My calc book says when you revolve about the x axis. The formula is S = | a to b (2pi (y) sqrt (1+(dy/dx)^2 ) dx = | a to b 2pi f(x) sqrt (1 + [f'(x)]^2 dx which is different than the way you figured it out. The answer looks correct just wish i understood why..
It doesn't matter what it's being revolved around. The problem gives you the limits in terms of either x (therefore dx integral) or y (dy integral). So you change the integrand accoridng to that. Also, the axis of rotation in this case only serves to show whether the radius is x or y. And then, you look at the limits given to see if it should be in terms of y or x. Hope this helps. To clarify, this is different than the traditional volume methods - which is why it's confusing.
At minute 4:17, you change the limits to [1, 145]. Correct me if I am wrong, that is done to allow us to work with smaller numbers... and it is not absolutely necessary to find the correct answer? Do you have any videos that focus on that technique? Ive seen it done in my calculus book, and Ive seen you do it a number of times, but Ive never been able to master it. Lastly, if you are looking for more topics to cover in your videos, there is a book used for "Applied Calculus II" called Basic Technical Mathematics with Calculus (by Washington). There are a few concepts in that book that I have only seen covered by a few videos; namely Fourier Transforms, if I remember correctly. Thanks so much for all the videos you've created. I know you are moving towards paywalls, etc. So be it, these videos are gold... absolute gold.
So the formula is this ____ and lets start solving questions with it... No Derivation, no examples of real world application, no minimal level of introduction and explanation....thats what I call great teaching by a great teacher...just Wow
Deriviation is important when you have like 8 seperate topic for an exam…you forget a formula??? Its ok just derive it. Real world application is important to get students interested in what they are learning. This guy just teaches how to solve these **SPECIFIC** problem, its your professor job to teach you the concept and everything else related to the topic
Thank you so much for making this video. I was having a really tough time and this video cleared it all up. I don't know what I would have done with out it. Thank you !!
I don't quite understand why we do not need to somehow substitute back in the value of the function for the radius when the solid is rotating on the x-axis but we are solving for y. If the function is x =*****y, would not the value of r(y) be *****y, instead of just r=y ?
Is R(x) or R(y) always parallel to the curve (or we want it to be /manipulate function)? I’m having difficulty understanding R(x) and R(y) so when it is equal to the given function or just equal to “x” or “y”
Why did you change the interval of integration around 4:50? If this is a common practice could someone tell me which video to watch. Thank you btw your videos are god sent.
Hey I was wondering if you could tell me how to derive the general surface area formula. (S = integral from a to b * 2pi * f(x) * Squareroot(1 + (dy/dx)^2) dx)
@@Bella-ul1fqi’m also 2 years late but at 24:53 he used u substitution and didn’t change the limits, can you explain why. Hope you do it before tmr cause that’s my exam
R(x) is the radius of the function. It was equal to y because the height of the function, is the function itself. So R(x) = y, and we were given that y is equal to x^3. I hope that makes sense
why are you updating limits? for example, at 4:45. why did the limits because 82 and 1? my teacher had the same problem solved buy kept his limits at 1 and 0 and got the same answer just wondering what the point is
@@ConceptualCalculus No he didn't. If he was revolving it around the y-axis, the radius would have been equal to the equation in terms of y. Revolving it around the x-axis, makes the radius the equation in terms of x, or just y.
I know I am no expert but you could have made DU/ 36= X^3 dx canceling out the x^3 as you replace DX. Just what I do to make things simpler and clean up my work
I'm curious as if to anyone tried solving the problem at 7:05 using U-Substitution. I tried and what is weird is that when I get to the steps of changing my bounds since I performed U-Substitution, my new bounds end up being the same [Lower Bounds: 3, Upper Bound: 3] I'm wondering if this happened to anyone else, and if there was a workaround about this.
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Application of Integration - Free Formula Sheet: bit.ly/3ZdKSnK
Calculus 1 Final Exam Review: ruclips.net/video/WmBzmHru78w/видео.html
Next Video: ruclips.net/video/TLw8xbmnY3c/видео.html
Whenever you say "In this video, we're gonna talk about..." I get a feeling that everything is going to be ok.
Lool me too brah😂😂
Lol
ave discorD?>
@Emerson Jabari both him and the other one are bots dont trust them
Me too 😂
I don't know why we gotta pay for tuition and crappy professors when we got this legend. They should honestly just assign these videos and give us the exams because that's basically what college has come to for me lmao. Thanks OCT for everything, you have no idea what you've got me through.
You're welcome
At least online schools without the need for classroom sessions exist.
The best part is when you get a job and they look at you funny when you try doing calculus and tell you to stick to your job ordering silicone. Not that I've had that experience or anything. Welcome to the world of proving your worth by suffering through math you don't need.
@@brynmrsh wait what happened
@@brynmrsh laughs in engineering major
Thank you for your time. You deserve the money that my school is getting.
maybe your school needs more money
Lmao
I swear I literally just search any topic from my class and your videos are first. You have everything. You. Are. My. Savior.
Bro I literally owe you my math classes, I started watching your vids when I was on 7th grade and now I'm a first year Civil engineering student. I gotta say your videos carried me a lot in my class. I swear when I get a job I'll donate a lot to you
Malawi?
Honestly I want to genuinely thank you so much for uploading your videos. You are very intelligent and a consummate teacher. you are so patient and sympathetic when you teach . Your videos have gotten me through Ap courses in highschool , and I would not be continuing my advanced courses without your lectures. Whenever I do not get something , I come to your videos. Words cannot explain how greatful and lucky I am to be able to view your videos . THANK YOU . I have never commented on any youtube videos before , but this is an expection , because your channel is my life savior . Keep doing what you do , all my classmates know about you , and we just have a study group and surround ourselves with your videos . We were wondering if you could do an Ap exam practice video before May 1st . We have a chemistry Ap exam and a Physics 1 exam on May 2nd . we have already watched your previous videos on a lot of the concepts you have made, and they were beyond helpful . The physics ap exam for us is different this year , I am in grade 11 , and they split the examination into two parts . Physics 1 includes all the grade 11 topics plus momentum , rotational motion , and i forget the last unit that was added , but I will let you. Please let me know if you could do this type of video , because I know a lot of people who would find this useful . Again , thank you so much for everything . I love you so much . If you need a schedule on what we learnt , let me know as well .
Yuki Mak SAME HE IS THE SAVIOR AND SAINT OF ALL EARTH
thats very true...he really helped
Thank you Thank you Thank you! Your videos have saved my Calculus 2 grade's life! It so easy to follow you step by step and some of the algebraic tricks you use are so helpful! Glad I found you on RUclips!
Thanks Jessica
I got below-average score for math when I took entrance exam (400/1000), but because of your video and I constantly watched and took notes from your videos, I got A for Calculus and even chemistry. Watching your videos, the complicated concepts become super easy, Thank you very much ;)
you, my friend, are a gentleman and a scholar.
I can't believe I'n just finding out about your channel now. You would have saved me when I was finishing my bachelor's degree in civil eng'g. But right now honestly you're helping me understand the concepts and basically right out solving problems that I literally would not have solved on my own. I'm about to take my licensure exams this coming November 2019 and you are saving my a$$! I can't afford to enrol myself in a review center, but here you are, offering your knowledge for free. Thank you so much and I hope you continue what you do, as you are obviously helping a lot of students not only pass their subjects, but to fully understand them as well. Kudos to you and God bless you!
you have no idea how much you helped me with my calc 2 homework. my own professor couldn't explain it this through!!!
Professor Organic Chemistry Tutor, thank you for another incredible video/lecture on Finding the Surface Area of Revolution in Calculus. I had problems with this topic in years past, however by doing a ton of problems and watching videos, my understanding of this material has drastically improved. This is an error free video/lecture on RUclips TV with the Organic Chemistry Tutor.
Got exactly what I came looking for. My textbook/professor has us memorizing different formulas for different orientations/rotations on the plane. Its much easier when these 'changes' in the formula were described as a radius of the circular slice.
Visualization>memorization
It took me awhile to figure out how that graph stuff works, but after that these equations became easier to solve. Thanks TOCT. If I pass my Calculus 2 this semester. I'm definitely going to show my support by donating. Appreciate it.
for the time 16:23 and on why is R(y) = y and not the whole x= equation that is given?
i was thinking the same thing.
mystery unsolved after years
@lilyfranks9839
I'm sure he made a mistake because f(y) is not equal to fx and he wants to flip around the x axis so he needs fx.
*goes to 2 and half hour calculus lecture*
Me: “I understand nothing..”
*watches 30 minute o-chem tutor vid*
Also me: “this shit is easy af”
Me watching 4 videos on my way to take my exam
Just a regular fella coming back for more help. Honestly bro you are amazing!
you're video has saved me at least 2 two days of reviewing!
You are a really intelligent teacher. I like your lectures and have learnt many things.
thank you so much, sir! you're saving my calculus grades
You have no idea how much I appreciate these videos, do you have anything on wave optics
I cannot watch your video without saying thank you.!! I learned a lot from your video, i mean, a lot!!!
Like I don’t understand why school has to make things so hard. Just help us to prepare for the test like this. We don’t need to know about the theories and all that. Just show examples, then explain why its like this. Thank you so much! This is much easier than I thought!
Question starting at 12:38. My calc book says when you revolve about the x axis. The formula is S = | a to b (2pi (y) sqrt (1+(dy/dx)^2 ) dx = | a to b 2pi f(x) sqrt (1 + [f'(x)]^2 dx which is different than the way you figured it out. The answer looks correct just wish i understood why..
It doesn't matter what it's being revolved around. The problem gives you the limits in terms of either x (therefore dx integral) or y (dy integral). So you change the integrand accoridng to that. Also, the axis of rotation in this case only serves to show whether the radius is x or y. And then, you look at the limits given to see if it should be in terms of y or x. Hope this helps. To clarify, this is different than the traditional volume methods - which is why it's confusing.
RUclips please, I graduated 2 years ago, why are you recommending me calculus videos
Came to this video bec I was stuck on an example.. and u solved the EXACT problem I was stuck on. I'm so happy haha
When I’m famous and rich, I’m buying you an entire country bro
Really You're amazing in Math .thanks a lot you save my time and my life too. Merci beaucoup
At minute 4:17, you change the limits to [1, 145]. Correct me if I am wrong, that is done to allow us to work with smaller numbers... and it is not absolutely necessary to find the correct answer? Do you have any videos that focus on that technique? Ive seen it done in my calculus book, and Ive seen you do it a number of times, but Ive never been able to master it.
Lastly, if you are looking for more topics to cover in your videos, there is a book used for "Applied Calculus II" called Basic Technical Mathematics with Calculus (by Washington). There are a few concepts in that book that I have only seen covered by a few videos; namely Fourier Transforms, if I remember correctly.
Thanks so much for all the videos you've created. I know you are moving towards paywalls, etc. So be it, these videos are gold... absolute gold.
So the formula is this ____ and lets start solving questions with it... No Derivation, no examples of real world application, no minimal level of introduction and explanation....thats what I call great teaching by a great teacher...just Wow
this is just how to solve these problems not to teach or explain the concepts, that’s for your professor/ if you buy his course
Deriviation is important when you have like 8 seperate topic for an exam…you forget a formula??? Its ok just derive it. Real world application is important to get students interested in what they are learning. This guy just teaches how to solve these **SPECIFIC** problem, its your professor job to teach you the concept and everything else related to the topic
You make everything soooo easyyyy!! Thanks for everything🤲💝
Thank you so much for making this video. I was having a really tough time and this video cleared it all up. I don't know what I would have done with out it. Thank you !!
the semicircle example is just genius
love this legend. the best thing in youtube
me at my commencement: I'd like to thank my parents, my professors, and especially the organic chemistry tutor
I don't quite understand why we do not need to somehow substitute back in the value of the function for the radius when the solid is rotating on the x-axis but we are solving for y. If the function is x =*****y, would not the value of r(y) be *****y, instead of just r=y ?
Is R(x) or R(y) always parallel to the curve (or we want it to be /manipulate function)? I’m having difficulty understanding R(x) and R(y) so when it is equal to the given function or just equal to “x” or “y”
did you figure it out? i also don't get it
Why did you not sub back in for u at 6:10? Can someone please explain? I am very confused about it
It is because he changed the limits. However, if you do not change the limits and leave it as 1 to 2 then you can sub back. I hope that made sense.
@@MikeTheGreatCC12 Yeah that makes sense. Thanks
@@MikeTheGreatCC12 thank you very much! that makes a lot of sense
What if the problem you showed:
x = (1/3)(y^2 + 2)^(3/2), 1
that's what i was just thinking
rotated at x axis = dx....
right?
conflict with the 1st problem in this video... 😵
got it... 😅
I dont even go class anymore. I just watch your videos
I cannot find videos about definite integrals involving the Surface Area of Revolution. What if you have 0
Why you always change the limits (e.g. a=1 and b=2) if you're going to use u-sub?
Gives all my money to a college to just have this guy teach me 😅
Why did you change the interval of integration around 4:50? If this is a common practice could someone tell me which video to watch. Thank you btw your videos are god sent.
if i got 145 as one of my integration limits i would immediately start freaking out that i had done the whole problem wrong XD
Hey I was wondering if you could tell me how to derive the general surface area formula. (S = integral from a to b * 2pi * f(x) * Squareroot(1 + (dy/dx)^2) dx)
3 years later.. did u ever come to understand it? I am there now lol
thanks you very much for saving me from failing in my calculus 2 quiz
I have a question, Why do u change the intervals in some of the examples but don't change it in other ones?
I know this is 2 years late, but you only change the limits when you use u-substitution to integrate :)
@@Bella-ul1fqi’m also 2 years late but at 24:53 he used u substitution and didn’t change the limits, can you explain why. Hope you do it before tmr cause that’s my exam
so basically R(x) is the same as f(x).....or am i wrong?
R(x) is the radius of the function. It was equal to y because the height of the function, is the function itself. So R(x) = y, and we were given that y is equal to x^3. I hope that makes sense
At 18:00 why didn't we change our bounds like in the previous problem?
Thanks man❤️ Love from Ph❤️
At 6:50
Wouldn’t it also be possible to square the number then cube it?
why are you updating limits? for example, at 4:45. why did the limits because 82 and 1?
my teacher had the same problem solved buy kept his limits at 1 and 0 and got the same answer
just wondering what the point is
13:00 If the video had stopped there, I knew that you are my h.s. teacher
slight anxiety from that
Your videos are so nice sir thanks a lot
12:57
In question no.3, if we are rotating the curve about x-axis then why would we take radius in terms of y rather than in terms of x?
He worked the problem as if it were revolved about the y-axes, although he said it was about the x-axis.
@@ConceptualCalculus No he didn't. If he was revolving it around the y-axis, the radius would have been equal to the equation in terms of y. Revolving it around the x-axis, makes the radius the equation in terms of x, or just y.
when rotated at x axis, is the strip dy? When rotated at y axis the strip is dx? please enlighten me, thank you
ı dont know how can ı meet you to say thank you
nway thank you Mr
Mastering volumes of revolution really helps before watching this video
Wow. This guy is a nerd. He knows all I need to know !
I know I am no expert but you could have made DU/ 36= X^3 dx canceling out the x^3 as you replace DX. Just what I do to make things simpler and clean up my work
I'm curious as if to anyone tried solving the problem at 7:05 using U-Substitution. I tried and what is weird is that when I get to the steps of changing my bounds since I performed U-Substitution, my new bounds end up being the same [Lower Bounds: 3, Upper Bound: 3] I'm wondering if this happened to anyone else, and if there was a workaround about this.
I believe there was a mistake at 11:18. You forgot to distribute the negative the -x^2 which would make the answer sqroot 4-2x^2
Sir After substitution what u did ?? and how limits are changed to 145 and 10
Does the radius and f prime both have to be in the same terms? (X's or y's)
Pretty much, because you have to integrate. Not saying there's not a case that wouldn't work
does that mean that instead of R(x) I can just write F(x) in the formula?
hello, regards daw si Jo sa imo kuya organic chemistry tutor
Hahahahaha
Hey is it possible to upload a calc 3 video about surface integrals?
Thank you ..its really helpfull
Thank you so much for making this video! It is excellent :) God bless
In 15:15 isnt the derivative of y^2= 2yy'? And not just 2y? Or is this not implicit
we are deriving with respect to y
Why are the limits of the curve being changed?
thanks a lot sir its very effective
Does anyone know why he used dy in the third problem if the task requires rotation around the x axis?
what if we wanted to calculate the volume sir? kindly share method
then u use disks and washers, shells
Find the surface area due to the rotation of the area between f(x)=x^3 and g(x)=x
Can anyone explain why in the first example why we change the limits of integration? First it's 0 to 2, then it becomes 1-145.
because we integrate by substituation
Ur Simply Juxt Owsm 😍😍
perfect one ,,thankyou
when is f(x) and r(x) different?
I really appreciate you
God bless you 😢💗💗✨ thanks a lot for your efforts 🫂🌸
Need questions with integrals involving trig and/or logarithmic functions.
Thanks Mr 🎉
Wait but why didnt you substitute U back in for the first problem?
why do we need to change the x values to u values??
We’re using a technique called U-substitution
Why doesn't just adding up the circumferences work? ie: ∫(2π*f(x))dx
dude in 21:53 if you draw the graphic correct, isn't R(x) going to be 2-x ? because R(x) + x = 2
in the first example, the u sub doesn't look correct to me, I'm getting a different answer.
I love this man
at the end of the video aren't you supposed to plug in "u" before plugging in the limits of integration
Thank you 🙏🏻
Bro. I love you.
if limit is not given then how to find limits? this is a problem
Thank you Sir
I think you made a mistake on the first problem. u was 1+9x^4. why do you directly substitute u as 145 and 1 at the end.
He changed the integration bounds because he is integrating in respect to u
very good..
Thank you
why did he not change u back into what he substituted into ?
Its also my question