Question

Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis.

x = 1 + (y - 2)^2, x = 2

Answer 1

Here's a link to my work:
https://www.dropbox.com/s/1krvexsi7smpgo7/6.3.%20%2311.pdf

Answer 2

Your setup looks right to me. Might be a typo, if that's the answer in the back of a book.