Mathematics

Problem

Region

R

in the first quadrant is bounded by

y=x

x=2

, and the

x

-axis. Cross sections perpendicular to the

y

-axis are rectangles whose height is twice the length of the base that lies inside

R

. Which integral gives the volume of the solid formed in this way? a)

\displaystyle \int_{0}^{2} 2\,(2-y)\,dy

\displaystyle \int_{0}^{2} 2\,(2-x)^2\,dx

\displaystyle \int_{0}^{2} 2\,(2-y)^2\,dy

\displaystyle \int_{0}^{2} (2-y)^2\,dy