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.
$$y = 1 + sec\;x,\;y =3,\;about\;y=1$$
How is the inner-radius of the cross-section $sec\;x$? Why isn't it $1 + sec\;x?$
Draw a rectangle representing the direction the function will rotate around the given line/axis.
Its easy to see that the rectangle formed will have the width $\delta x$ and height $y+1 - 1 = (\sec x + 1)- 1 = \sec x$