When to use Disk vs Shell vs Washer

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To determine when to use the Shell, Disk, or Washer methods for integration, start by sketching the problem and choosing an axis for integration that simplifies the process. Analyze the cross-sections along that axis to identify whether they resemble disks, shells, or washers. The choice of method may vary based on the complexity of the integral, as some methods may require splitting the integral into multiple parts while others do not. Experience and visualizing the problem are key to making the right decision. Ultimately, practice and understanding the geometry of the problem will lead to clarity in choosing the appropriate method.
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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.
 
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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.
 
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?
 
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.
 
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.
 

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