cylindrical shells (1 Viewer)

[ashokkumar]

when finding volumes using cylindrical shells, how do you determine the upper and lower limits for the integral? :S

 

[adomad]

you observe how the shell moves... post up a Q

 

[YannY]

So basically for cylindrical shells you are making cylinders perpendicular to your non rotational axis. Thus parallel to your rotation axis. The key here is to note which axis it's perpendicular to because essentially thats how many shells you are making. technically speaking, you are trying to make infinite shells to find the exact volume. But for simplicity we can assume that there are a limited number of shells within every 1 value of boundary.

So you're adding up all these shells thus the boundary must be the one that the shells are perpendicular to.

Anyhow, if you didn't understand the general rule is that for slicing the boundary is the same as the rotational axis and for shells its the opposite of the rotational axis.