Chapter 6, Problem 27RE

Volumes of solids Choose the general slicing method, the disk/washer method, or the shell method to answer the following questions.

27. The region bounded by the curves $y=1+\sqrt{x}$, $y=1-\sqrt{x}$, and the line x = 1 is revolved about the y-axis. Find the volume of the resulting solid by (a) integrating with respect to x and (b) integrating with respect to y. Be sure your answers agree.