The region bounded by the curves and for is revolved about the horizontal line

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

Problem

The region bounded by the curves

y = x^{2}

and

y = 2x

for

0 \le x \le 2

is revolved about the horizontal line

y = -3

. Which integral represents the volume of the resulting solid? (a)

\displaystyle \int_{0}^{2} \pi\bigl[(2x)^{2} - (x^{2})^{2}\bigr]\,dx

(b)

\displaystyle \int_{0}^{2} \pi\bigl[(2x - x^{2})^{2}\bigr]\,dx

(c)

\displaystyle \int_{0}^{2} \pi\bigl[(2x + 3)^{2} - (x^{2} + 3)^{2}\bigr]\,dx

(d)

\displaystyle \int_{0}^{2} \pi\bigl[(x^{2} + 3)^{2} - (2x + 3)^{2}\bigr]\,dx