A solid has cross sections perpendicular to the -axis defined as follows: • For

MATHEMATICS · Single correct · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

A solid has cross sections perpendicular to the

x

-axis defined as follows: • For

0\le x\le 2

, each cross section is a square whose side length is

s(x)=x+1

. • For

2< x\le 4

, each cross section is a rectangle whose height is

3

and whose base is

b(x)=x

. What is the exact volume of the solid, in cubic units? (a)

28

(b)

\dfrac{80}{3}

(c)

22

(d)

\dfrac{98}{3}