Mathematics

Problem

Consider the region bounded above by the horizontal line

y=2

, below by the line

y=x-1

, and between

x=0

and

x=2

. The region is revolved about the x-axis. Which of the following best describes the integral setup needed to compute the volume of the solid? a)

V=\pi\int_{0}^{2}\bigl[2^{2}-|x-1|^{2}\bigr]\,dx

V=\pi\left[\int_{0}^{1}2^{2}\,dx+\int_{1}^{2}\bigl(2^{2}-(x-1)^{2}\bigr)\,dx\right]

V=\pi\int_{0}^{2}2^{2}\,dx

V=\pi\int_{0}^{2}\bigl[2^{2}-(x-1)^{2}\bigr]\,dx