Washer method rotating around vertical line (not y-axis), part 1 | AP Calculus AB | Khan Academy
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Setting up the definite integral for the volume of a solid of revolution around a vertical line using the "washer" or "ring" method. Created by Sal Khan.
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For anyone curious this is used in calculus 2 for college level lol
can confirm
His drawing skills have definitely improved from the early integral videos.
You can see it like: phi is for the 180º degrees, the semicircle; and square is for the simetry that covers the other negative side of the axes. That's one way to picture it
what would happen if you rotate around a negative vertical line, (x=-2, would it be 2+y^2)?
Absolutely
thank you sir
Bruh I’m struggling so hard in Ap calc and my exam is literally in like a month and a half or so 💀
whatd you get on the exam
@@kiwi9660 a 2 😁🔫
@@podojeff4797 oh crap
Way better than my college math teachers!
Thanks!!!!
THANK YOU. SO. MUCH!
I can't find the next video but I got the answer to be pi(191/30). Roughly 6.4*pi area units, a bit much perhaps?
was the answer 31/30 pi?
where's the next video
this is first year calculus for courses like engineering (im doin chem eng)
hope u failed out u nerd
nobody cares
Got a job yet? I'm first year now
what about if the axis is on the negative side? would it then be y^2-2 and sqrt(y)-2 or would it still be the same
add the distance between y-axis and x=line. Basically, you're moving the functions to be revolving around y=0.
So is the outside radius always the function farthest away from the axis of revolution?
Most useful video
I’m doing this in high school and no longer have motivation I have 30 days of school left 😢
at 7:34, is there another way to get the integral numbers (2 and 0) without visually looking at a graph? Graphing it can take a little long during an exam.
Yes you can equal the two functions with each other and then find the values of y
czcams.com/video/i-Rb4_n929k/video.html
Part 2 of this
where is the other half of y = x^2????
does anyone know how to do this with respect to x? (using dx instead of dy)?
Matthew Tran not sure if there is a way because you’re rotating it around a vertical line, meaning you’ll need to find the area between the function and the vertical line with respect to y.
Actually never mind, you can by using the shell method.
Wait, why isn't the outer radius 2-sqrt(y) and the inner radius 2-y^2?
Because the outer radius corresponds to the function furthest from what your revolving around
I learned this for Calculus AP which is technically a highschool course. Otherwise I believe its a first year Calculus material.
I'm watching this as a first year Ivy League engineering student, I don't know if engineering is my future if I already need to watch Khan's vids -_-
+Fiasco Even engineers have trouble understanding hard concepts. Don't get discouraged, we all learn differently.
what college?
General Ouki Cornell.
haha take L O S S
The answer is 31pi/30 by the way
I think the answer is 61pi/30
I'm sorry I disagree heavily. That is not orange that is salmon pink
Oh snap, I messed this up
Now I have -10 p on my test :S
what did you get overall?
Was that important to make the explanation so messy and confusing...