The volume is given by the integral
\(\displaystyle2\pi\int_1^2x(9-(1+x^3))\,\mathrm dx=2\pi\int_1^2(8x-x^4)\,\mathrm dx\)
with the shell method, and
\(\displaystyle\pi\int_2^9((\sqrt[3]{y-1})^2-1^2)\,\mathrm dy=\pi\int_2^9((y-1)^{2/3}-1)\,\mathrm dy\)
with the washer method. Both integrals give a volume of \(\dfrac{58\pi}5\).
