Mathematics

Problem

A solid rests on the region between the

x

-axis and the graph of

y=\sqrt{x}

from

x=0

x=5

. Cross sections perpendicular to the

x

-axis are defined as follows: • For

0\le x\le 2

, each cross section is a rectangle whose height is

4

times its base. • For

2< x\le 5

, each cross section is a square. Which of the following integral expressions gives the volume

V

of the solid? a)

V=\displaystyle \int_{0}^{2} 4\sqrt{x}\,dx+\int_{2}^{5} \sqrt{x}\,dx

V=\displaystyle \int_{0}^{2} 4x\,dx+\int_{2}^{5} x\,dx

V=\displaystyle \int_{0}^{2} 4x\,dx+\int_{2}^{5} x^{2}\,dx

V=\displaystyle \int_{0}^{5} 4x\,dx