When to use Disk vs Shell vs Washer

[duki]

Can someone explain to me when you should user the Shell / Disk / Washer methods? I don't understand how to determine which method to use.

 

[Dick]

Sketch a picture of the problem. Pick an axis to integrate along that looks like it will be the easiest. Now look at the cross sections of the area along that axis. Are they disks, shells or washers? You can do it more than one way. The picture is the most important part.

 

[duki]

I often sketch the picture and can't decide which method to use. Is there a way to tell which will be easiest for the given sketch?

 

[Dick]

About the only difference is sometimes one method will require you to split the integral into multiple parts and another won't. There's no method I can describe in words, looking at the picture and experience will tell you.

 

[duki]

You know how sometimes you think about stuff for like three hours and can't figure it out... but then all of a sudden something just "clicks"?

That just happened... Thanks for your help!
I'm going to wait to mark this as solved to make sure I got it down.