# What is the surface area produced by rotating f(x)=2x^2+4x+3, x in [0,3] around the x-axis?

$V = {\int}_{0}^{3} \pi {r}^{2} \mathrm{dx}$
$= {\int}_{0}^{3} \pi {\left(2 {x}^{2} + 4 x + 3\right)}^{2} \mathrm{dx} = \frac{19535 \pi}{3}$