<p>for the ap calc bc exam, do you have to know how to use cylindrical shells? my teacher didnt teach it to us because he said its off the ap requirements and you only need the washers/disk method. is that true, or should i study it anyways? thanks.</p>
<p>yes that is true, but you should only study them if you think you're pretty comfortable with other big topics such as diffeqs, parametric/polar, series, fundamental theorem, approximations...</p>
<p>shells come in handy usually when your differential is parallel to the axis of revolution. It's useful if you're lazy like me and don't feel like interchanging variables (the volume question on the AP test almost guarantees that you only have to integrate w/ respect to x) the formula for the shell method is also very easy to apply and it should only 20-30 minutes to get understand the formula and do a problem or two.</p>
<p>You should definitely memorize the formula and know how to apply it: you technically don't need it for the AP exam, but it can be very helpful on a lot of problems.</p>
<p>The key is the representative cross-section:</p>
<p>If your cross-section lies parallel to the axis of revolution, shells will work. If your cross-section lies perpendicular to the axis of revolution, discs/washers will work.</p>
<p>The direction of your cross-section will frequently be based on what's easier to work with. For instance, in cases where y is a function of x, you tend to use discs/washers around a horizontal line, but shells around a vertical line.</p>
<p>The way you get around using shells when you want to revolve around a vertical line is to solve that function for an x = equation as a relation of y.</p>
<p>In some cases, transferring from one form to the other is difficult, and so the AP folks have basically guaranteed that you can always use a discs/washers form, while the shells form might not always work.</p>
<p>That being said, if you have the time and feel comfortable with the normal stuff, shells might be easier than discs/washers on a particular problem, and some students prefer volumes by shells to discs/washers, even if the calculations aren't necessarily "easier".</p>