Okay, so, I think I am getting the hang of these problems. Would anyone care to check? All we are required to do for the homework is set up the integral.

; about the x-axis

I set up my graph. It is the graph of a parabola with line y=1 going horizontally through it, and x=0. Seeing this, and the fact that it was solved in terms of y, I set up the integral in terms of a R and L volume. Integral is 0 to 1.

I got:

Am I correct?