A solid has base in the region under the graph of from to

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

Problem

A solid has base in the region under the graph of

y=x

from

x=0

x=2

. At each value of

x

, the cross section perpendicular to the

x

-axis is a triangle whose base equals

x

and whose height is

(2+x)

times the base. What is the volume of the solid? (a)

\dfrac{28}{3}

(b)

\dfrac{10}{3}

(c)

\dfrac{14}{3}

(d)

\dfrac{32}{3}