Longer Version - Volumes using Cylindrical Shells
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- čas přidán 1. 12. 2008
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Longer Version - Volumes using Cylindrical Shells - In this video I do numerous examples of finding volumes using the shell method.
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I learned more in this 20 minute video than my 1 hr university lecture. Thanks Patrick!
SpiritedBanana me too😂😂😂
SpiritedBanana lol same
1 hr lecture in 20 minutes
Its sad that as university students paying thousands in tuition have professors that are so fundamentally bad we have to seek online teachers to help us. THANK GOD we have you patrick, without you i won't pass this calc2 class.
T Mccart imagine the hardship in the early 90's hahaaha where youtube is not that popular (or does not exist yet, not sure). They have to rely on their prof and book to pass this course.
didn't your father teach you how to read a textbook? teachers work better with the book
welp ya usually are just paying for the degree
Dropped that super casual bomb - "Always make your shell the parallel to your axis of rotation." That was amazing, and very helpful!
pearls of wisdom
I've gotten two 100% scores in my Calc 2 class because of you. I always feel lost in lecture but you always make it so simple and easy to follow. I'm really thankful for your videos, you're awesome!
You are such a better teacher than my Calculus teacher, thanks.
A friend of mine recommended your videos. I've been getting C's in calc lately, and for one who has never gotten below a B, I rather dislike that. Even 5 minutes in, it already makes more sense than when my calc teacher explains it. Thanks!
happy to help. i have tons of calc 2 and 3 stuff, so come back any time.
patrickJMT you are my senpai
For anyone wondering, multiplying the 2pi in front comes from multiplying each shell cross section by the circumference of the shell (since circumference is 2pi*r, it just brings out the 2pi). That was something I didn't understand at first, so I thought I'd share it for anyone else who might be wondering :)
You mean circumference?
XNagelX Oops, circumference* Yes. Thanks for pointing that out!
XNagelX
i dont under stand the concept of shell radius
I read your comment, didn't click, took a break, it clicked.
the clearest demonstration. I was lost in the class, but after watching your videos, I understand.
Thank you so much.
When it comes to calculus revision - there is no one better. Thanks a lot for the help friend.
Thank you soooo much!!! If I pass my cal2 exam in 2 hours, it's all thank to you. Such simple concept, why cant teacher explain it simply like this.
+Annie Do good luck!!
Your way of teaching is like you're babysitting a math student. I love it!
Dude I have been watching videos trying to understand this for 4 hours and you freaking saved my life
The BEST video out here on Cylindrical shells includes all possible cases. Amazing thank you so much!
Thank you so much for this video. You have no idea how long it has taken me to understand this. This is my third time taking calc 2 and third time is a charm because of you. I have understood everything in calc 2 except the volumes, and areas. Your videos are helping me get my degree.
I forgot how to do this after learning it in class in a 90 min lecture, I remembered within 6 min of your video. May God Bless you.
Ahhh.... The beauty of understanding math.
Thank very much you man.
You're even the first channel I subscribed to.
Now... numberphile and minutephysics...
In 100 years, when youtube is gone and the internet is replaced by virtual reality, struggling calc students are still going to be watching this video. Thanks Patrick!
Wow! Thanks, patrickJMT ! I remember learning this during my lecture and the prof was trying to explain this but it only made things worse. Came home thinking I was going to fail the exam but then I came across your videos. You're a life saver :) Thank you once again :)
Once again, Patrick, you come through and save the day. This video helped me A LOT to understand shells. Thanks SO MUCH! :D
I was loosing my mind to understand how to get shell radius but after spending 5 min watching this video everything became crystal clear. Thanks man.
words can't describe how much thankful I am for your videos.
Have been watching your videos my entire way through calculus. Thanks you really help!
spent hours on my homework and kept getting the wrong answers, watched this video, and then BAM! i started to get all the right answers. You are the man
Tomorrow is my semester's mid. I've been browsing your videos the last 1 hour about the trig identities/Volumes/Areas and if I do pass tomorrow it'll be because of you. You are a life saver. What is even more surprising is that we spend thousands of bucks on professors which barely could make math interesting. Though this video is about 10 years old, but you are still a legend. Keep up the good work, fam. (Y) May God Bless you.
so did you end up passing?
I dont even know why i have lectures, you make calculus so much easier to comprehend, THANKS SO MUCH!
your way of explaining is just so fantastic and easy to understand and even memorize , thank you so much
I'm a tutor myself, and I just wanted to say you're a good teacher man. Thanks for your awesome vids and well spoken explanations/instructions.
You have no idea how much this helped me
+Phalgun Krishna they are academics, all they care about is their research and their job. Some of them do not have the gift of teaching. therefore, professors are not hired for their teaching abilities but for research at a university.
Some professors on the other hand, have the teaching ability and we are truly blessed when we have them :D
+franco diaz thanks, but I'm in high school. I'll definitely keep that in mind though next year.
@@phalgunkrishna2467 how was campus?😅
great thorough video that covers multiple situations. Much appreciated!
you are a life savior! i always go on your page when i need help with my calculus. thanks so much!
great video man. Thanks for doing the multiple examples. Especially the ones with the different "about x" and "about y" lines. I also liked how you did the (shell radius) * (shell height) thing. You don't know how long I spent studying the book to no avail and I finally came across your video. I'm doing a 1 block summer Calc 1 class and I don't have time to waste and this saved me. Thanks
From the bottom of my heart thank you very much. It turns out that the way you explain makes things easier to me.
Saved my Life!! Craming for a calculus midterm and was so lost.
yea, some of the early videos had some audio issues! sorry, only a few do this!
you are one of the best teachers I have ever seen in Calculus. always making my life with the Math in the university much easier, THANKS A LOT ..
You sir, are my hero!!! My teacher doesn't know how explain anything, so I watch your videos instead! You understand that just because you understand it doesn't mean we do, so you actually explain it, unlike my professor! He thinks because he's a know-it-all, we should be too, but we're not! So thank you so, so much!!
you are the best. seriously. Such a life saver. My prof does not make sense but you just made it so easy in 20 minutes THANKS SO MUCH!
Rotating About Y-axis --> Cylindrical Shells Method Wins
Rotating About X-axis --> Disk/Washer Method Wins
Just checking but is this due to the fact that you don't have to convert the y= x equations to x= y form or something else?
crazylazy007 yup, you are right. That's the reason. But sometimes in very rare cases, it depends on the equation too like sometimes shell method might simplify things when rotating about x axis....but in general ya...its gud to use as mentioned above
crazylazy007 when the problem you trying to solve is in the x-axis you will have to convert the y=x to x=y
in the last example when it rotating about y=-3 . i use disk/washer and it shows a different answer. idk why ?
Geez thank you for this. It actually makes sense coming from another
You are a great teacher. I wish your were my Calc 2 professor!
So a general rule of thumb is to express the functions in terms of y if rotating about the y-axis and express functions in terms of x if rotating about the x-axis? Is this the opposite of the disk/washer method?
never had this clear explanation ever!
I've fallen in love with your voice
Thank you for telling me what I NEED to know and not all That other theory garbage my teacher goes into. U have the most helpful math vids on youtube, and for that, I thank you.
This video was really helpful. It really explained how to solve for volume. I get alot of help from my teacher but sometimes i need help when im notbin her class and this video really helped
you're so good at teaching, that i am able to explain this stuff to other people. your teaching is contagious
Your handwriting is just beautiful... It literally brought tears to my eyes!
why don't we do that outer radius^2 - inner radius^2 to get the height? as we did in washer method?
Just tried this on the washers and disks section and it did not work for those. When it is about one of the axis, we keep useing x or y for shell radius right? thats the only possible place of error I can think of.
what is ' a ' ?
Freaking fantastic. You are a life saver. I was so confused by all of the different methods. you ROCK.
thank u so much for posting this video. it helped me a a lot. there were some things my professor wasn't so clear on but now i get it. thanks
I have to say, you are really great. I thank you so much for all of your videos!!!
Thank you for all of the effort you put in this!
I didn't know anything before this, (missed a week of class) your vid is a life saver.
My life wouldn't be complete without you!
Thank you so much :) Your videos are always so helpful :)
@PhxPride1 it comes from the formula for the circumference of a circle
Wish I would've seen this months ago! If I pass my calc class, it's gonna be thanks to you! Thanks for all the vids.
You've got one of the neatest handwriting I've ever seen, lol.
And thanks a ton!! This way of remembering the formula as "shell radius" and "shell height" helps a lot more than the way our teacher taught us (p(y) and h(y)...then the outer/inner difference is w, you do w/2 and it got too confusing). this is plain and simple. Ty again!! :D
i never go to calc lectures anymore I just watch patrickJMT and get enlightened
Thanks... I was having a hard time finding the radius but i am already ok
Thank you so much! I was feeling really terrible, because I couldn't understand, but you make it seem so easy!!!
Dude you are the man. I didn't understand a thing before I watched this. Thank you!
THANK YOU!!!!!!!!!!!!
Wow I have watched at least 15 of your videos already, great job!
I need to be spoon fed math to learn most effectively. I wish I had known about you for calc I.
Wow, the last 2-3 weeks of calc have been like sitting through a Chinese class. These last 3 days of watching your videos have translated all that into English haha, I just wish I had stumbled upon your videos about a week ago, I'd be a lot more prepared for my final. Thanks for what you do, it is greatly needed and appreciated.
you are fantastic, thank you so much! my teacher only gave examples involving rotating around the x and y axis only so i had no idea how to go about revolving other axis's and how to deal with other stuff you addressed, thanks !!!
i always recommend you to my classmates! you make calc so much simpler, thank you
Best teacher I've ever had!!!
You are the reason I will be passing Calc 2. Thank you for your kickass explanation that does not go into unnecessary theory like my professor!
Hi Patrick I have a question. how do i solve it if it rotates about x=1?
What a teacher you are i have never seen I like it sir your this lecture
This lecture more useful for me for exam point of view
You are so much smarter and better at teaching than my professor! I wish you were my professor!!!!!
What happens if the thingy you made does not touch the y axis and you have to rotate it along the y axis? Do I need to add something(shell radius+__)(shell height) or leave it be as (shell radius)(Shell height)
i pass my maths because of you Pat
i learned so much more about this chapter in here than my calc 2 class. thanks man
Thank you very much for all of your videos. I just made a small donation on your website and want to encourage others to do so. Tutoring at this level would be VERY expensive!
What if the solid between the two curves doesn't intersect with the origin like it did in your examples? Is the the shell radius just x in this case if you were to rotate the solid about the y axis?
You make my calc life so much easier! Thank you so much! :D
Hello! I have a question. I will always use the "cylindrical cylinders" when the cylinders formed are parallel to the axis of revolution, or who can be used when the cylinders formed are perpendicular?
You are the most amazing man on the earth. Thank you so much, my prof did NOT explain this very well!
I have A calc exam today and my only hope for passing is your videos
you sir, have a Gift. God bless you man, you have basically saved me from the horrors of my midterm! and everything else :)
@AmberinTrees glad it helps!!
was confused. now. everything is clear. YOU DA MAN!
Quiz in 4 and a half hours... and i feel pretty confident now... nice videos...
hey +patrickJMT! do you have any videos tackling on the topic of the centroids of solids of revolution?? BTW, your vids always help me pass my subjects.
Awesome tutorial ---easy to understand and easy to remember ---better than my class teacher
This is so clear, you're just great. Thanks so much!
You broke it down nicely, thanks!
Hello Patrick, what would I do to find the limits of integration when the area is bounded by more than 2 functions?
How do you know when to use the disk and washers formula or the cylindrical shells formula for these types of problems?
your teaching was down to earth, you are gifted to teach. may God continue to increase your knowledge of the subject. i say amen to it.
hey man thank you so much and thank god your calc teacher haha im having mi final exam tomorrow, and i never got 2 understand this during the semester and i learned it on you tube!!!! thnks so much
I really think you are great, thank you so much for these videos and making my life so much easier.
dude by far .......... the easiest guy to understand thankks a lot ....
@kalasko14 glad it made sense : )
Thank you this helped me so much!!
great stuff.; really nice to see the Shell Radius explained.
awesome, thanks for your lectures.
For the problem at 5:49, what would the new limits be once you use the u-substitution?
And thanks i needed some help, i have to present shell method and disc method to my class so im going to explain it this way :)