I'm trying to find the volume as shown in the picture I've attached. First of all, would I have to set the functions equal to x rather than y since the figure goes up and down and not left to right, and second of all, I know I'd have to subtract two integrals of something since the figure is hollow in the middle, but I don't know which I'd subtract from which.
is the distance between a representative rectangle and the axis of revolution (i.e., the distance between and the line ). In other words, it is the average radius of the shell corresponding to each particular value of
Had you been revolving about the -axis, that factor would just be for revolution about it would be (2-x), and so on.