Mathematics

Problem

Let R be the region bounded by the curves

x=y^{2}

and

x=2-y

. For each

y

between

-2

and

1

, a square is constructed with base lying in R and with its sides perpendicular to the y-axis. Find the volume of the resulting solid. a)

\displaystyle\frac{9}{2}

\displaystyle\frac{81}{5}

\displaystyle\frac{81}{10}

\displaystyle\frac{81\pi}{40}