Mathematics

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

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

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

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