The instructions for this question verbatim are: "Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer."
I believe the domain is $-\pi/2$ to $\pi/2$
I've been having a really hard time visualizing the functions for the radius of the inner and outer rings. I've graphed the function and the lines but I'm still stumped. I thought that the formula for the outer radius would be $\pi(2)^2$ because the outer radius is always 2 units away from the line of rotation, and the inner radius $2-(1+\sec x)$. With these equations I end up having to find the anti-derivative of 2 sec x which we haven't done in class. This makes me think I'm wrong about one of the expressions - likely the inner radius. Do you have any advice for understanding how the expressions for the inner and outer slices are affected by the point of rotation?
It would probably help to first graph the functions so you can visualize the region you are rotating. You can do this via online graphing programs or a graphing calculator if you have one. Does the question specify which quadrant/interval to look at? I ask because $y=1 + sec(x)$ intersects $y=3$ at many points.