Volume by Shell Method and Washer Method

Instructional video for Briggs/Cochran Calculus 2e. The text features hundreds of videos similar to this one, all housed in MyMathLab. Visit www.pearsonhighered.com/briggscochran2einfo for more information.

[@complex314i]

When you do the rotation around x = -.25 by the washer method, you should mention that the bounds y=0 and y=1 must be found by finding the y values at x=0 and x=1. Without mentioning this, many student will mistakenly think that shell and washer methods have the same bounds.
Example:
If we have f(x) = 3-x^(1/2) from x=0 to x=9 for shell, we have y=0 to y=3 fir washer.

[@Kay-dx8vm]

I swear that all my A grades are earned from watching youtube videos. Thank you for your clear explanation, sir

[@jstnnnnn]

The graphs made this easy to visualize. Thanks!

[@gratitudeisanattitudechaud9383]

It's helpful for me

[@abdulrakeebalsarori8171]

Brilliant! the graphs, everything is just excellent! Thanks a lot!

[@shathaal-omari2910]

You saved my life😭😭😭

[@bostangpalaguna228]

Thank you so much.. The visualisation really help

[@scaslx]

Great explainmentation! Also, your voice is so charming!!

[@lynnhtetkyaw2788]

nice and unique explanation! thank u very much

[@academicstuff548]

great video sir.

[@tpstrat14]

Close your eyes and visualize it. Let god or “the universe” show it to you. That’s the only way I
got through this. In fact, I never once looked at any visuals outside of my own head. See the function and that’s it... revolve it in your head then turn it around in your head to see it from all angles. Concentrate, let it come. You can do it!

[@barismetin1014]

awesome video!

[@emenikeanigbogu9368]

great video

[@birdtweet1]

what a god

[@musawaleed224]

Amazing

[@jaskiratsingh1970]

it was really amazing ....

[@Zhangweifang817]

the only video shows why is it called washer and shell in shapes :)

[@wahidhamidy6886]

thank you so much sir

[@ceprodarisystem5051]

Great!

[@Guitardudeftw]

In the washer method, what determines whether it is dx or dy? Does it depend on wether it's rotated horizontally or vertically?

[@migipatel4862]

The axis does determine if its dx or dy. I think if it's rotated horizontally its dx and if its vertically its dy because the equations would need to be in terms of y.

[@williamnathanael412]

Rotating about the x-axis, use dx for Washer method and dy for Shell method. About the y-axis, dy for Washer and dx for Shell. Treat horizontal lines as x-axis and vertical lines as y-axis.
Bonus: in what respect do we integrate when we are calculating volume of solid of revolution about a diagonal line?

[@aseelalsinjo7097]

SinQ/cosQ

[@brantleykerns3968]

increase speed to 1.25 and its so much better