Shell method for volume of revolution (rotated about different axis and lines)

Shell method for the volume of revolution. We will cover 7 calculus 1 homework problems on using the shell method to find the volume of the solid of revolution from the Stewart Calculus textbook book. This calculus tutorial will help you if you are taking calculus 1 or ap calculus AB.

Hint, it's easier to use the shell method than the disc/washer method when we are given y=f(x) and we rotate about the y-axis or a vertical line.

0:00 y=x(x-1)^2, rotated about y-axis
3:24 y=sin(x^2), rotated about y-axis
6:04 y=cbrt(x), rotated about y-axis
9:23 y=x^(3/2), rotated about x-axis
13:20 y=4x-x^2, rotated about x=1
19:43 x=2y^2, rotated about y=2
25:54 y=tan(x), rotated about x=pi/4

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#justcalculus

[BITStudioCode]

Lowkey these things get really satisfying to get right on delta math when you know how to do it. It just goes pop and pop and there you go. I do these problems just by analyzing them and then popping them into the calculator and then bam!

[Meganisherelol]

LITERALLY SAVED ME BEFORE MY FINAL EXAM THANK YOU SO MUCH

[JR-lxes]

You are so amazing!!! The visuals helped immensely and now I know what region needs to be shaded and how to reflect it. Sending many blessings your way!

[aleksandergeiger]

Thank you. You managed to teach this better in 30 minutes then my professor did over 2 weeks.

[simplemathguy]

Great Video! Thank you sir! I struggle with this topic but after watching 3 of your videos about disk/washer, and shell method, I enlightened. May God bless you sir! MORE SUBSCRIBERS TO COME!

[hmedina]

I like your delivery and presentation. I subscribed and will look for your videos in the future. Thank you!

[machoslothman]

thank you math papa, you have been a life saver for my grade

[BITStudioCode]

Our ap calc BC teacher said this was good to know, I can see why now haha!

[dominickcross]

Can somone explain why on the last problem x was pi/2- x? I get from the y axis to the axis of ration being x but not where the pi/2 xome from if the y equation was tanx

[noahanderson]

crazy that cylindrical cells aren't part of the AP Calc curriculum. They expect you to find the inverse function and revolve that using washer integration instead.

[jedzou]

Thank you, sir. After 2 years, we still find this vedio useful for me!

[Loleeh]

thank you for making this helped me <3

[smallcoffeetheday]

Why did i try to use disc method on problem 3 and it give a different result. Can someone help me, i got 1, 25 but not 2, 69

[JamesBrodski]

Great video! Thank you for making it :)

[mcbananabread]

how would you solve using the shell method when one y value is your equation, another y value is a whole number, and your x value is 0 (about the y axis)?

very similar to the problem you solved at 9:33 but about the y axis.

[MusayerohBah]

I'm saved, thank you so so much!

[CyCloNeReactorCore]

at 14:31, why were you just able to move the 3 over to the other side, instead of subtracting it on both sides? is because the equation equates to 0, and I just didn't know that you can do that?

[adhritimandal]

Are these old videos bcoz i can't see your beard😃😃?

[carlostadeocanela-terrazas]

este video es pura confusion no sirve el maestro