Mathematics

Problem

Let

S

be the union of two regions in the first quadrant. For

0\le x\le1

S

is bounded by

y=x

and

y=x^{2}

. For

1\le x\le2

S

is bounded by

y=2-x

and

y=x

. Cross sections perpendicular to the

x

–axis are squares. What is the volume of the resulting solid? a)

\dfrac{7}{6}

\dfrac{4}{3}

\dfrac{41}{30}

\dfrac{31}{30}