A cross-section is a washer with inner radius [tex] 3[/tex] and outer radius [tex]x^3 + 3[/tex]
[tex]V = \int_0^1 A(x)\, dx = \int_0^1 \pi\left[ (x^3+3)^2 - 3^2 \right]dx = \int_0^1 \pi\left( x^6 + 6x^3 \right)dx \\ \\
= \pi\left[ \frac{1}{7}x^7 + \frac{3}{2}x^4 \right]_0^1 = \pi\left(\frac{1}{7}+ \frac{3}{2} \right) = \frac{23}{14}\pi[/tex]
