Consider the region bounded by the curves and for

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

Problem

Consider the region bounded by the curves

y=kx

and

y=x^{2}

for

0\le x\le k

, where

k>0

. Squares are erected on this region with bases perpendicular to the

x

–axis; the side of each square equals the vertical distance between the two curves at that

x

–value. If the volume of the resulting solid is

8.1

cubic units, what is the value of

k

? (a)

3.6

(b)

2.5

(c)

3.0

(d)

2.4