The Shell Method | Calculus 2 Lesson 4 - JK Math

[@noreldenzenky1527]

i think there is a mistake at the time 46:15 the therms should in y because the revolution about y axis by disc method

[@JKMath]

Good catch! My apologies on that mistake. You are correct, since we are revolving around the y-axis, the integral should be entirely in terms of y for the disk/washer method. Can't believe I didn't catch that when I edited this video, especially since I correctly set up the first integral in terms of y, but not the second. To fix the mistake, solve for x in the function y=x^2+1 to get x=√(y-1) as the inner radius and substitute that in for where I put x^2+1. And then of course, there should be a dy instead of dx at the end of the integral. Thanks for pointing this out, again, my apologies on this mistake and any confusion it may have caused.

[@noreldenzenky1527]

@JKMath you are great go on sir

[@sayefalikhan529]

you are a life savior, man. I just wanna say thank you. Now I understand the concepts very well because of you. This is the best channel on yt for learning maths. keep doing what you're doing.

[@JKMath]

You're very welcome! And thank you for the kinds words, I appreciate it :)

[@rajrcit]

Why so less views 💀 on a masterpiece

[@dustedcaramel]

keep doing what you’re doing bro, this helps me so much

[@JKMath]

Thank you, I appreciate that. Glad the videos help! Will definitely continue to make more :)

[@Rozhan_Fard]

You explain so well! very organized and easy to understand 🙏🏻Thanks JK Math!

[@JKMath]

You're welcome!

[@africaplayer1]

I just wanted to say thank you... You are saving my life with your calc videos!

[@JKMath]

You're welcome!

[@AD-wg8ik]

Thanks! Watched khan academy first, and it finally clicked with this video

[@OverclockingCowboy]

This is a question on average radius r at 4:30. Normally r is just equal to x. Instead of x, can we just use (a+b)/2 which is the actual average radius? Conceptually, we can take the area bounded by f(x) from a to b multiplied by the thickness 2pi(r) where r = (a+b)/2.

[@JKMath]

No, the radius always needs to be defined in terms of x, it will not be constant. I see why you would think it could be (a+b)/2, but remember that in that diagram I drew, that was just ONE cylinder that is representative of many cylinders we are using to find the volume using the shell method. So each cylinder will have a different average radius. That's why we need to use x, as the average radius of each cylinder will be dependent on where those cylinders are located along the x-axis. You can test this out with the example problems in this video, if you change the radius from x to (a+b)/2 you will get a completely different answer, and it will be an incorrect answer. Hope this helps!

[@OverclockingCowboy]

@@JKMath Thanks for the reply.

[@MuscleMedia7]

Love you sir ❤

[@darkdayformeofcause9608]

THANK YOU SO MUCH! This help me a lot with my final test!

[@JKMath]

You're very welcome, hope your test went well! :)

[@miralawwad2642]

you saved me thank you

[@OmPrakashMaharana326]

It's very informative, i love your videos

[@JKMath]

Glad to help! :)

[@angieg7257]

Best video!

[@AsadRajpoot-f4b]

In example 3 part 1 , function revovlves around y=1, means along x axis why we not set the function equals to y , while in previous methods (disk , washer) we set it =y

[@JKMath]

I'd recommend you rewatch the beginning of this lesson video, as it will make this much clearer for you. In short, the shell method works differently than the disk or washer method. When revolving around a horizontal axis in those methods, you worked in terms of x, but it is the opposite for the shell method. You will instead work in terms of y. Hope this helps!

[@AdelinaGeorge-i7r]

This was amazing, thank you so much!!

[@JKMath]

You're welcome! Glad the video could help :)

[@AsadRajpoot-f4b]

do u have uploaded chap 10 sequence and series

[@JKMath]

Yep, I have videos covering sequences and series in my Calc 2 playlist! You can find it in the playlists tab on my channel.

[@AsadRajpoot-f4b]

@@JKMath thank u

[@ahsokatano5394]

Thank you so much

[@JKMath]

You're welcome!

[@Mister-l3j]

Is radius always “y” or “x”?

[@JKMath]

The radius is neither "always" x or y. It will depend on the axis of revolution. If you are revolving around the x-axis, then the radius is y, but if you are revolving around the y-axis, then the radius is x. BUT, if you are revolving around a line that is not the x or y-axis, then you need to adjust the radius accordingly as I explain starting at 25:02. Hope this helps!

[@Mister-l3j]

@ yes I got what u mean , may God bless you

[@kelliamaral6891]

Just thought I'd point out that you don't even need to use an integral to find the area of the bottom part - it's a rectangle!

[@ritvikindupuri2388]

For Example 1 why is the height not 1- x^3 as the height would be the distance from x=1 to y=x^3

[@JKMath]

Since we are revolving around the y-axis, the height will be measured in terms of x, so you want to look up and down the area, not left to right. From this we can see that the height is between the x-axis and the curve, so the height is just the function that represents the curve, just like I labeled it in the video. Hope this helps!

[@ritvikindupuri2388]

@@JKMath I see it’s mainly cause since X is a vertical line we have to look up to down rather than side to side (y=)

[@JKMath]

@@ritvikindupuri2388 You could think of it that way, sure. But in general when working in terms of x, you look from up to down, and when working in terms of y, you look from right to left.

[@ritvikindupuri2388]

@@JKMath oh i see

[@Protonm0KEN]

It's cool

[@NathanCarlson-l4j]

Like this comment if you are here from my class