Let R be the region bounded by the curves and

MATHEMATICS · Single correct · IB Diploma Programme · Mathematics: Analysis and Approaches · Calculus · Calculus

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}

(b)

\displaystyle\frac{81}{5}

(c)

\displaystyle\frac{81}{10}

(d)

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