Like problem 8-55, the rotating radius will be horizontal (because the axis of rotation is vertical). Consequently, the bounds of integration will be y-values: from y = 1 to y = 13. Both the bounds and the integrand will be written in terms of y.
Unlike problem 8-55, there will be a cylindrical hole in the center of this 3D figure. This hole has a radius of 1.
Unlike problem 8-55, the outer function is no longer f(y). It is 1 unit longer than f(y).