Mathematics

Problem

A solid has base on the interval

0\le x\le \pi

along the

x

–axis. Above each

x

[0,\pi/2]

, the cross section perpendicular to the

x

–axis is a square whose side length is

\sin x

. Above each

x

[\pi/2,\pi]

, the cross section is a rectangle whose base is

\sin x

and whose height is three times its base. What is the volume of the solid? a)

\dfrac{\pi}{2}

\pi

\dfrac{\pi+12}{4}

\dfrac{3\pi}{4}