When the shaded area is rotated 360° about the x-axis, we again observe that a volume is generated:

Applying the above formula, we get

`{: (V,=pi int_a^b y^2 dx), (,=pi int_0^3(x^3+1)^2 dx), (,=pi int_0^3(x^6+2x^3+1) dx), (,=pi [(x^7)/(7)+(x^4)/(2)+x]_0^3), (,=pi(|355.93|-|0|)), (,=1118.2\ text[units]^3) :}`