Question

Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the curves y=x−1 y=0 x=2 and x=5 about the x-axis.

Answer 1

Using disks ...
$V= \pi \int\limits^5_2 {(x-1)^{2}} \, dx =\pi(\frac{1}{3}(5^{3}-2^{3})-(5^{2}-2^{2})+(5-2))=21\pi$

The volume is 21π units³ ≈ 65.97 units³