Volumes of Revolution - Cylindrical Shells
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- Опубліковано 24 сер 2024
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Volumes of Revolution - Cylindrical Shells. In this video I show to examples of finding volumes using the method of cylindrical shells.
As GREAT as these videos are, I have to say his voice is very soothing, which isn't so great in the late hours of the night haha
i do it for love of the stupid comments i receive.
i just wanted to say that my TUTOR couldn't teach me this, but YOU can. thank you so, so much. you are a lifesaver to those mathematically impaired like myself.
Thanks so much, huge help. Nice to see someone help so many ppl on the internet instead of posting garbage all the time
After watching a lot of your lessons in the past few weeks, i feel like you're one of my best buddy
so i've been trying to do these problems for a good two hours and this is the ONLY thing that has made sense to me all day aah. you are my hero? check
I'm a substitute teacher teaching calculus tomorrow.
You have saved me a lot of time, and improved the quality of my teaching.
THANK YOU SO MUCH!!! :)
you have made sense out of the supposed gibberish in two minutes (i got it midway through the video) what i've been trying to learn through 2 one hour sessions of caculus! thanks so much!
you should become a teacher and or tutor if you are not already you explain everything so perfectly
I just learned something great, when you rotate about something that is not about and axis (x, or y) you can simply go~~~ integral of (X-c)( f(x) - g(x) )dx where "c" is the value of your rotational axis, so if your rotating about x = -3 like this example, you just plug in and its (x+3)( f(x) - g(x) ) just like Patrick does. Just thought id let you guys in on some possible helpful knowledge
Patrick your a god keep doing what your doing!!!
you are an angel sent to save all calculus students
you are the best math teacher in the whole existence of the universe
well, who am i to argue? (thanks for the kind words!)
Patrick! Your videos are so helpful that I would send you heaping piles of boxes of dry erase markers just so you could keep on doing what you do! You helped me through one tough semester of calculus, here's to two more! THANK YOU!
Oh my goodness. You are an angel! I had so much trouble with cylindrical shells. Thank you so much! I'll probably watch the rest of your videos to help me study for my AP exam. Thank you again!
I got a test 2maro and you may have just saved my ass, YOU F@$%ING ROCK MAN!!!
i've watched your videos throughout all of cal 2! My exam is tomorrow so I'd just like to say thank you for being the best cal teacher I ever had!! :D
Thank you for acing my finals for me, semester after semester.
Thank you for being beautiful! Wanna grab coffee?
Sandor Clegane you want to grab coffee with flowers? I think they prefer water.
Less than 1 hour before my calc final and You sir have saved my ass
much easier conceptual presentation than my crappy book. great work!
Tomorrow is AP Calculus Exam and thank you so much for the brush up! ^.^
Thanks. A trick to remembering which way you draw the shell is you draw it "parashell" to the line your going about. Thats how I remember it :D
Patrick thanks for makin all these videos. You've helped me pass my math classes since the middle of high school. Hopefully you get the opportunity to teach at a university if you don't already. I'd transfer to your university just to take your class instead of listening to people that don't know what they're talking about. keep it up!
Thank you!! you broke a foreign language down to understandable regular English! I've had the hardest time getting this concept. You explained it well.
@Matthew Carr The line one revolves an equation by does not matter so much, because it all depends on how the cylindrical shells will look or be placed. It becomes more of a sense as how the shells would fit best in the created figure. Whether it is best to have the shells in a horizontal (dy) or vertical (dx) position.
I personally prefer yours to the Khan Academy. Thanks so much!
Bless you Patrick. For allll of your free guidance. Bless you.
You're videos are perfect for brushing up or learning something new. I should already know this like the back of my hand, but I honestly don't even remember half of it haha.
You definitely need to be a teacher AT MY SCHOOL
Thanks for the explanation about why you added the "+3" in the second example. I could not for the life of me understand why the radius changed when you go around a different line.
I have really appreciated your videos on the Shell Method.
Thanks for taking the time to record and post these.
Seriously man, thank you so much. You make things so much simpler than my professor.
Exactly! As you probably know 2(pi)(r) is the circumference of a circle but in this case x is our r, think of x (the radius) as an arbitrary variable that changes as the block that patrick drew in the video moves farther and farther away from the line that the shell is rotating about (in this case the y-axis) hopes this helps!
like many other souls of innocent calculus students you have saved me from failing
Well done .. Bro .... Your conveying method is one of the best😍😍😍
got a test in a few days. after this, like WTH if I get any less than 100%! i came here even after watching the MIT lecture (which was a little confusing).
THANKS!
Oh and 5 people failed Calculus.
Thank you so much, its the 2nd video I've watched.Just subscribed.Thank you once again for taking your time off to help us.
Excellent video. You've saved so many people patrickJMT. I hope beautiful women of your likings physically pleasure you an absolute maximum (math term there, lol). You've saved so many people.
Keep up the good work. And for the future PLEASE put up more complicated examples of various topics in calculus. That's how we learn, from seeing and doing various examples. School only repeats the mediocre examples they give from the mediocre book.
your are a very wonderful person for taking your time to help others! thanks again for all the help!!
That's great man, a lot better than most! I've used Patrick for the tougher concepts. It's a six week course here, but so far I got a 74 and 100 on my first 2 exams. I'm really scared for my next and final exams.
Your voice sounds so deep here Patrick! Thank you for posting these great videos.
in general, both methods can be used for either the X or Y axis; often times though, one method will be much easier
A huge thanks to u !!
i don't know what i have to say ! ..
BTW : i did good at today exam .. thxxx : )
keep going bro .. : )
@yerikim0413 but you're forgetting the "+x" term. When factorised, as already mentioned, y=x(1-x). This means that the roots of this equation are 0 and 1. Using the symmetry property of quadratics, the maximum (because the coefficient of x^2 is negative) will be at x=(0+1)/2 = 1/2. When x=1/2, y=1/4. Therefore, the graph cuts the x axis at x=0 and x=1 with a maximum turning point at (1/2, 1/4). The graph shown is correct in shape. Hopefully that has eased your mind. :)
practice examples seem so easy and simple, but the test be super hard
Because the guy fails to address critical points of introducing a new math concept, which is why and when we need to apply this concept. if you want more info on this you can check my channel.
@@montrealmathandphysicstuto2807 stay in your lane bro
@@imGhLz learn to communicate properly
@@imGhLz no he is right. Patrickjmt shows the best way to have an algorithm to find the solution. Other youtubes, although might be more convuluted would have a more theoretical approach for deeper understanding
you can always 'use it' regardless of the axis - often times one way will be easier to integrate though
Dude i hope i pass my integral calculus~! i clearly understand the way you explain each of this information about cylindrical shells...
You just saved my ass on a huge Calc II test... THANK YOU
Sir Patrick , i know its tooooo late to say this but THANK YOU !!!!! , You really helped me !~
Your videos help make the concepts clearer and I have found my grades in calc helped by them:D
You explain it so well. Thanks for all these posts!
cause the radius varies depending on how far you are from the y axis. you should read the proof/derivation of the formula from your book to understand it better.
bro, after weeks of confusion over this concept, you have finely broken the line between me understanding it and not!!!!
Why is it that most math teachers are completely and utterly ineffective at teaching basic concepts in higher-level math in person, while smart people such as PatrickJMT can use a dry-erase board to teach effectively?
this is awesome man, you rock really. Way better than my calculus 2 teacher.
@LosVideosDeLouis happy to help :) good luck in the rest of your classes!
thanks for the quick review. my final is tomorrow morning. this really helped bro!
@kcuf0000 Basically you use disk/washers method when rotating about the x-axis and shells when rotating about the y-axis...., but technically you can use either one, depending on the case you could also just interchange the variables....hope it helps
Here goes nothing, taking my calc 2 final in two hours. Thanks @patrickJMT
It all just made sense. Thank you so much.
good luck!
7π/6 for the last question
I'm starting to love integral calculus because of you :)))
You're a superhero.
In the second example, I think you have to integrate with respect to dy.... since the rotation goes around the x-axis. please correct me if i am Mistaken.
good luck with the class!
@xxcowslayerxxx i have never seen a question like this. it would be confusing as to what exactly one means if they were to do this. it would also depend heavily on the geometry of the object
Thanks for helping me get through Cal 2 :)
You're a freaking life saver
Thank you very much! I like math more because of you :)
glad you liked it :)
@nikvenkata cause you are ' x ' units away from the y-axis
Your videos are SO SO SO helpful!! =]
everybody is doing last minute cramming!!! good luck everyone!!!!!!!!!
Man, YOU ARE AWESOME!!! Thanks a million for your awesome help :)
As always, a perfect explanation. Thanks!
Wow my teacher was like the 2 pi times the integral of h(x)p(x) where w is the width of the rectangle and p is the distance from the axis of revolution to the center of the rectangle and h is the height when we dont even know wtf the rectangle is. thanks
It's about the y-axis. The x-axis is horizontal and y-axis is vertical.
i love this channel , patrik you are great man , u helped me a lot , thank you man
This helped me A LOT, thanks!
Thanks a lot patrick!!!!
I wish I found this BEFORE I took my test over volumes by integration...
For the second example, does it matter if you increase the radius or height? As opposed to just the radius.
OH MY GOSH YOU'RE A LEFTY!!!!! Thank you!!! :DDD
glad to help!!
Can you explain why we use dx even though we rotate around the y - axis? When trying to find volumes by discs or washers, we would use dx for the x - axis and dy for the y axis. Here I don't get why its dx for y and dy for x.
Hypothetically, would it be incorrect to use dy and put everything in terms of y? Albeit more difficult, you would still get the same answer, no? I am referencing the point you made about rotational axes at approximately 1:08 in.
@atimor ha
You should change your name to patrickJMTA-Just Math Tutoring and Awesomeness
@SSerju ha, just a normal guy trying to help out
If you wanted to revolve about x=1, would the setup be 2(pi) * integral from 0 to 1 of (1-x)(-x^2+x)??
So whenever you rotate about the y axis or any vvertical line, your radius is gonna be x?
Hello, I do not understand why you are integrating with respect to x when rotating about the y-axis? Thanks
Great job 🌹
nice! i wanna hear it
@zainabbeans ha!
Thank you
watching it 4 years later
HVALA TI .... means Thank You in Bosnian
I love you Patrick
Thank you for your good explanation. I was confused why turning axis and integrated variable is different. Now I understand for this video.
However, I have a question for geomatrical meaning of shell method. Little bit confused between shell and disk. May I ask for your explanation? :)