Find the volume of the solid generated by revolving the described region about the given axis:
The region enclosed above by the curve https://webwork.math.uga.edu/webwork2_files/tmp/equations/23/88cfb3fea3d8c8579f5a0608e8bd751.png, below by the https://webwork.math.uga.edu/webwork2_files/tmp/equations/fe/7ca85459d2390dbf4a5dfdd0b8b8e91.png-axis, to the left by the https://webwork.math.uga.edu/webwork2_files/tmp/equations/85/067ce783e2f89ced535d722b824af51.png-axis, and to the right by the line https://webwork.math.uga.edu/webwork2_files/tmp/equations/bd/6693b22701966f67dede0ee6737cf71.png, rotated about the https://webwork.math.uga.edu/webwork2_files/tmp/equations/85/067ce783e2f89ced535d722b824af51.png-axis.
We had been going over Volumes of Cylindrical Shells, so I'm pretty sure we need this formula
Integral from a to b = 2pi(shell radius)(shell height)dx
The Attempt at a Solution
I made a nice graph of the equation, but I don't understand the constraints. Under the x-axis, to the left of the y-axis, and to the right of x = 2 makes no sense to me. Under the x-axis and to the left of the y-axis is Quadrant 3, but to the right of x = 2 is Q1 or Q2. I've been looking for examples in my book like this, but none of them are similar to this. I'm pretty sure once I understand the area it is talking about then I can do the rest myself.