1. washers vs shells

I am having a hard time visualizing when i would want to use the washer method vs the shell method. I know it is a case by case basis, but if anyone could give me some rational way of approaching rotational volume problems and making the decision of washers vs. shells that would be great!

Thanks!

2. I like to think of it this way:
If you're rotating equation f(x) around the x-axis (or any lines parallel to the x-axis), you would use the washer method.
If you're rotating equation f(x) around the y-axis (or any lines parallel to the y-axis), you would use the shells method.
If you're rotating equation f(y) around the y-axis (or any lines parallel to it), you would use the washer method.
If you're rotating equation f(y) around the x-axis (or any lines parallel to it), you would use the shells method.

So basically if you're rotating an equation whose differential is the same as the axis you're rotating (for example rotating f(x) around x-axis or f(y) around y-axis), you would use washer.
If they're different (like rotating f(x) around y-axis or f(y) around x-axis), you would use shells.

Hope that helps.