Need Help Understanding Disk/Washer/Shell Setups

[Silvanoshei]

Here's the problem to base the usage of each on.

Let R be the region bounded by the curve \(\displaystyle y=\sqrt{x}\), the line \(\displaystyle y=1\) and the y-axis. Find the volume of the solid generated when the region R is revolved:
(a) around \(\displaystyle x=-\frac{1}{2}\)
(b) around \(\displaystyle y=1\)
(c) around x-axis.

The first thing that pops into my mind is the Washer Method, because it can get rid of that nasty sqrt sign fairly easy with it's ^2 notation. Drawing it is fairly simple, I'm really confused on the rotation bit though. Could I use Washer Method on all 3 cases? Or is there a better approach to each rotation?

 

[DrPhil]

Here's the problem to base the usage of each on.

Let R be the region bounded by the curve \(\displaystyle y=\sqrt{x}\), the line \(\displaystyle y=1\) and the y-axis. Find the volume of the solid generated when the region R is revolved:
(a) around \(\displaystyle x=-\frac{1}{2}\)
(b) around \(\displaystyle y=1\)
(c) around x-axis.

The first thing that pops into my mind is the Washer Method, because it can get rid of that nasty sqrt sign fairly easy with it's ^2 notation. Drawing it is fairly simple, I'm really confused on the rotation bit though. Could I use Washer Method on all 3 cases? Or is there a better approach to each rotation?

Often times you can use either washers or cylinders. Washers will work for all of these. BUT don't count on the radical going away when the axis is x=-1/2.