A solid has rectangular cross-sections perpendicular to the x-axis

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

Problem

A solid has rectangular cross-sections perpendicular to the x-axis. At a particular value of

x

, the base of the rectangle in the

xy

-plane extends from

y=2

y=5

, and the rectangle’s height at that

x

is given by

h(x)=3x

. Which of the following expressions gives the area

A(x)

of that cross-section? (a)

A(x)=3x+5-2

(b)

A(x)=21x

(c)

A(x)=3x(5-2)

(d)

A(x)=\tfrac12\,(3x)(5-2)