Mathematics

Problem

The base of a solid is the region bounded by the graph of

y=\cos x

and the

x

-axis on the interval

0\le x\le \pi

. Cross sections perpendicular to the

x

-axis are described as follows: • On

0\le x\le \tfrac{\pi}{2}

, each cross section is a rectangle whose height is

2

units and whose base equals

\cos x

. • On

\tfrac{\pi}{2}<x\le \pi

, each cross section is a square. Which of the following is the exact volume of the solid? a)

3

2+\dfrac{\pi}{4}

\dfrac{\pi}{4}

2+\dfrac{\pi}{2}