Mathematics

Problem

A solid has base the region bounded by the graphs of

y=x

and the x-axis on

0\le x\le 2

. The cross-section perpendicular to the x-axis at each

x

is a rectangle whose height

h(x)

is defined by

h(x)=x^{2}

for

0\le x\le 1

and

h(x)=2-x

for

1<x\le 2

. Which of the following is the volume of the solid? a)

1

\dfrac{11}{12}

\dfrac{5}{6}

\dfrac{13}{12}