Volumes of Revolution using Cylindrical Shells
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- Опубликовано: 12 сен 2024
- Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) / patrickjmt !! Calculating volumes of revolution using cylindrical shells. Examples are shown of regions rotated about horizontal and vertical lines.
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You are a blessing on this world, I swear it. I binge so many hours of youtube videos because my professor never shows up to lectures, so all I have to work with is youtube and my textbook- which seldom makes sense if ever. Whenever a concept is really busting my butt, I can always count on one of your videos explaining it in a way that I can ACTUALLY grasp, and for someone with mental disabilities and the most uncaring professor imaginable, that's incredible I think. I owe you a heck of a lot more than just ad revenue, someday when I'm not an impoverished college student, I will have to donate you a hefty sum of cash.
thanks for the kind words, happy i could help you out a bit :)
I'm grateful that people like you make these videos. My lecturer doesn't even know how to send a damn e-mail, let alone use any technology to teach Calculus. This will be what saves my grade this semester!
You're a gazillion times better at explaining this than my professor. Love you x
Hello patric , I really want to thank you about these tutorials . They are really helpful and easy to understand . I passed calculus 2 and 3 with 80% , however, I failed calculus 1 last year because when I first started college I actually had no idea of how the exams would probably be and would it be difficult or not and my level was too bad tbh . As a civil engineering student , calculus was so important to me and our prof exams were extremely tough tho I studied harder and passed calc2, now I am retaking calculus 1 and hopefully I pass it with a good grade . I never forgot last semester's calculus ..Jacobian and double triple integrals and series tests😂 . It was so fun though it was tough . By the way thank you again :)
I cannot express my gratitude for this video.
THANK YOU VERY MUCH I'M CRYING
Confusion finally clarified. Thank you 💞
this really helped me alot ! i just understood all my homework problems from your little tutoring here ! the part that helped me most was the idea of shell radius and shell height ! thank you so muchhh !
You can factor out constants, the formula for shells is the integral of: 2pi(radius)(height), by pulling out the 2pi, it changes nothing, just makes it more friendly to look at :)
@Damitajoey :)
@DUNK6AROO : ) i try
at 14:40 to find the interscects for y, which is what you put in the intergral, you can just set the two functions/curves equal to each other? y^2 = y
y^2-y=0
y(y-1)=0 -> y=0, y=1
I'm getting this now, I hope.
,OMG I LOVE YOUUU. I thought I'd never work it out
Thank you thank you thank you thank you thank you
where did you get the limits of integration?
Such a great help! Thank you!!!
i survived math since highschool because of you..im now in college. A million thanks to you sir
thanks for sharing light on the basics of integration
shading
Thank you, this is very useful. I feel much better prepared for my quiz.
wow! how amazing does is look to come across useful video, I wish I could see this tutor for real, you are amazing buddy,
There's a 2pi in front because, when you make a shell, u get like, this weird almost cylindrical looking thing. And the volume of a cylinder is V=piradius^2*height. It was mentioned in this video that the radius is x so we have pix^2*height. I cant exactly remember what happened to the height but basically pix^2 was derrived and we get 2pix, x being the radius. Or something like that, i'm no expert. >.
So for the first example if it was rotated about the x-axis. Would the shell height be "root(pi)" and radius "sin(x^2)"?
wouldn't you integrate with respect do dy since you're rotating about the y-axis? or is that only with washers/disks?
when you use Shell method, is all the way around, you have to integrate with respect to dx if we are rotating about y axis. the height is always parallel to the axis we are rotating about.
Disk method is used when your radius is perpendicular to the axis you're revolving around..Hint-- f(x)=x about y axis requires shell and f(x)=x about x axis requires disk
Hi, just wondering whether Cylindrical Shell Method or Disk/Washer Method can be applied in solving Double Integral problem in finding volume??
was watching videos, quietly and patiently ... 15:16 ... "OMG!" *jump off of seat* lol
God bless you sir
Thanks for the video it helped quite a lot.
AWESOME EXPLANATION. VERY HELPFUL. THANK YOU. U R D BEST :)
I missed my teachers lesson on the shell method. his notes were shit. Thanks alot!
Why is there 2 pi out in the front?
Can you use this method instead of the washer and disk methods??
If so...
Is it easier?
at 15:35 do we always have to twist that way? because if we twist the other way we get a diff height
it's very useful for me :3
thank for your video !!!!
Patty, you're the BOMB!!!
hey patrick, any tips on how to set up these problems.
i find myself stuck depending on the situation.
still don't get the damn radius part. This is gonna fk me in the exam -.-
im having sooo much trouble with radius also
Sabrina Perez It's always going to be simply x or y, unless you're rotating off the y or x axis. Then it's simply the the axis of revolution - x or y if it's above or to the right of your whole function. It's the axis of revolution + y or x if it's below your function. for example: if you're rotating about the axis x=2, and the function was to the left of this distance, then simply write 2 - x. if we change the axis to x=-2, then just write 2+x.
5 month later but perhaps other people will see it. The radius is literally the radius of a Cylinder. Superimpose a cylinder of that graph directly on the y-axis and you will see the part labeled radius is simply the radius of the cylinder. The only reason this works is because we can superimpose a cylinder on top the graph and pretend we are solving for volume of a cylinder. Pi * R^2* H = Vol Cylinder Literally just superimposing that equation over the integral.
RG Calderon haha hope you passed the class. it took me a while to get it down too when I was first learning it.
Imagine you have the circumference of your cylinder, now slice the cylinder open and roll it out like a carpet, its no longer a cylinder anymore, but a rectangle . The side length of the rectangle = the circumference= 2pi(r).
you the real mvp bro
I think i'm gonna pass my integral cal subject! Thanks! ❤️
Thank you 🙏
oh thank you!!!!!!!!!!! this video is best!
sir plz tell me the reason that when you rotate about y-axis, why you take limits of x-axis
y=1 and y=0 are the points of intersection for the graphs as well
Anisha Nagpal
how would you rotate it about x=1?
Wow u r good and perfect cal teacher for m
15:16 WARNING HEADPHONE LISTENERS!!!
T S Thanks for the warning. I thought I'm all prepared, my headphones were 2 inch away at that time, but I got startled also.
THANK YOU!!!!!!
well said
amazing thank you
wouldnt it be -y-y^2 not y-y^2 because if we flip it, it would be x=-y
i will be here next time you get stuck :)
thank you
thaanku g thanku
Need help with radius!!!
Why do you have 2 of these same videos on your channel?
Thank you life safer ♡
damn, now everyone is going to get an A in Calc
merci bcp :))
Calculus 2 CCP
Ooooooooooohhhhhhhh... I get it. Thanks! :)
sorry!
Audio
thank you